[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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[9939] | 13 | !! zdf_trd : diagnose the zdf velocity trends and the KE dissipation trend |
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| 14 | !!gm ==>>> zdf_trd currently not used |
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[456] | 15 | !!---------------------------------------------------------------------- |
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[5836] | 16 | USE oce ! ocean dynamics and tracers variables |
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[9019] | 17 | USE phycst ! physical constants |
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[5836] | 18 | USE dom_oce ! ocean space and time domain variables |
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[9019] | 19 | USE sbc_oce ! surface boundary condition: ocean |
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[5836] | 20 | USE zdf_oce ! ocean vertical physics variables |
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[9019] | 21 | USE zdfdrg ! vertical physics: top/bottom drag coef. |
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| 22 | USE dynadv ,ONLY: ln_dynadv_vec ! dynamics: advection form |
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| 23 | USE dynldf_iso,ONLY: akzu, akzv ! dynamics: vertical component of rotated lateral mixing |
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[9490] | 24 | USE ldfdyn ! lateral diffusion: eddy viscosity coef. and type of operator |
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[5836] | 25 | USE trd_oce ! trends: ocean variables |
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| 26 | USE trddyn ! trend manager: dynamics |
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| 27 | ! |
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| 28 | USE in_out_manager ! I/O manager |
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| 29 | USE lib_mpp ! MPP library |
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[9939] | 30 | USE iom ! IOM library |
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[5836] | 31 | USE prtctl ! Print control |
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| 32 | USE timing ! Timing |
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[456] | 33 | |
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| 34 | IMPLICIT NONE |
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| 35 | PRIVATE |
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| 36 | |
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[9019] | 37 | PUBLIC dyn_zdf ! routine called by step.F90 |
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[456] | 38 | |
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[9019] | 39 | REAL(wp) :: r_vvl ! non-linear free surface indicator: =0 if ln_linssh=T, =1 otherwise |
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[456] | 40 | |
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| 41 | !! * Substitutions |
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| 42 | # include "vectopt_loop_substitute.h90" |
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| 43 | !!---------------------------------------------------------------------- |
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[9598] | 44 | !! NEMO/OCE 4.0 , NEMO Consortium (2018) |
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[1152] | 45 | !! $Id$ |
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[9598] | 46 | !! Software governed by the CeCILL licence (./LICENSE) |
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[456] | 47 | !!---------------------------------------------------------------------- |
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| 48 | CONTAINS |
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| 49 | |
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| 50 | SUBROUTINE dyn_zdf( kt ) |
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| 51 | !!---------------------------------------------------------------------- |
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| 52 | !! *** ROUTINE dyn_zdf *** |
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| 53 | !! |
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[9019] | 54 | !! ** Purpose : compute the trend due to the vert. momentum diffusion |
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| 55 | !! together with the Leap-Frog time stepping using an |
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| 56 | !! implicit scheme. |
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| 57 | !! |
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| 58 | !! ** Method : - Leap-Frog time stepping on all trends but the vertical mixing |
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| 59 | !! ua = ub + 2*dt * ua vector form or linear free surf. |
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| 60 | !! ua = ( e3u_b*ub + 2*dt * e3u_n*ua ) / e3u_a otherwise |
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| 61 | !! - update the after velocity with the implicit vertical mixing. |
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| 62 | !! This requires to solver the following system: |
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| 63 | !! ua = ua + 1/e3u_a dk+1[ mi(avm) / e3uw_a dk[ua] ] |
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| 64 | !! with the following surface/top/bottom boundary condition: |
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| 65 | !! surface: wind stress input (averaged over kt-1/2 & kt+1/2) |
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| 66 | !! top & bottom : top stress (iceshelf-ocean) & bottom stress (cf zdfdrg.F90) |
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| 67 | !! |
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| 68 | !! ** Action : (ua,va) after velocity |
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[456] | 69 | !!--------------------------------------------------------------------- |
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[9019] | 70 | INTEGER, INTENT(in) :: kt ! ocean time-step index |
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[3294] | 71 | ! |
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[9939] | 72 | INTEGER :: ji, jj, jk ! dummy loop indices |
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| 73 | INTEGER :: iku, ikv ! local integers |
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| 74 | REAL(wp) :: zzwi, ze3ua, z2dt_2 ! local scalars |
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| 75 | REAL(wp) :: zzws, ze3va ! - - |
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| 76 | REAL(wp), DIMENSION(jpi,jpj,jpk) :: zwi, zwd, zws ! 3D workspace |
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| 77 | REAL(wp), DIMENSION(:,:,:), ALLOCATABLE :: ztrdu, ztrdv ! - - |
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[456] | 78 | !!--------------------------------------------------------------------- |
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[3294] | 79 | ! |
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[9019] | 80 | IF( ln_timing ) CALL timing_start('dyn_zdf') |
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[3294] | 81 | ! |
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[9019] | 82 | IF( kt == nit000 ) THEN !* initialization |
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| 83 | IF(lwp) WRITE(numout,*) |
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| 84 | IF(lwp) WRITE(numout,*) 'dyn_zdf_imp : vertical momentum diffusion implicit operator' |
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| 85 | IF(lwp) WRITE(numout,*) '~~~~~~~~~~~ ' |
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| 86 | ! |
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| 87 | If( ln_linssh ) THEN ; r_vvl = 0._wp ! non-linear free surface indicator |
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| 88 | ELSE ; r_vvl = 1._wp |
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| 89 | ENDIF |
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| 90 | ENDIF |
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[9250] | 91 | ! |
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[9939] | 92 | z2dt_2 = rDt * 0.5_wp !* =rn_Dt except in 1st Euler time step where it is equal to rn_Dt/2 |
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| 93 | ! |
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| 94 | ! |
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[9250] | 95 | ! !* explicit top/bottom drag case |
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| 96 | IF( .NOT.ln_drgimp ) CALL zdf_drg_exp( kt, ub, vb, ua, va ) ! add top/bottom friction trend to (ua,va) |
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| 97 | ! |
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| 98 | ! |
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[9019] | 99 | IF( l_trddyn ) THEN !* temporary save of ta and sa trends |
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| 100 | ALLOCATE( ztrdu(jpi,jpj,jpk), ztrdv(jpi,jpj,jpk) ) |
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[7753] | 101 | ztrdu(:,:,:) = ua(:,:,:) |
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| 102 | ztrdv(:,:,:) = va(:,:,:) |
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[456] | 103 | ENDIF |
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[9019] | 104 | ! |
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| 105 | ! !== RHS: Leap-Frog time stepping on all trends but the vertical mixing ==! (put in ua,va) |
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| 106 | ! |
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| 107 | ! ! time stepping except vertical diffusion |
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| 108 | IF( ln_dynadv_vec .OR. ln_linssh ) THEN ! applied on velocity |
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| 109 | DO jk = 1, jpkm1 |
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[9939] | 110 | ua(:,:,jk) = ( ub(:,:,jk) + rDt * ua(:,:,jk) ) * umask(:,:,jk) |
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| 111 | va(:,:,jk) = ( vb(:,:,jk) + rDt * va(:,:,jk) ) * vmask(:,:,jk) |
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[9019] | 112 | END DO |
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| 113 | ELSE ! applied on thickness weighted velocity |
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| 114 | DO jk = 1, jpkm1 |
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[9939] | 115 | ua(:,:,jk) = ( e3u_b(:,:,jk)*ub(:,:,jk) + rDt * e3u_n(:,:,jk)*ua(:,:,jk) ) / e3u_a(:,:,jk) * umask(:,:,jk) |
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| 116 | va(:,:,jk) = ( e3v_b(:,:,jk)*vb(:,:,jk) + rDt * e3v_n(:,:,jk)*va(:,:,jk) ) / e3v_a(:,:,jk) * vmask(:,:,jk) |
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[9019] | 117 | END DO |
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| 118 | ENDIF |
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| 119 | ! ! add top/bottom friction |
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| 120 | ! With split-explicit free surface, barotropic stress is treated explicitly Update velocities at the bottom. |
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| 121 | ! J. Chanut: The bottom stress is computed considering after barotropic velocities, which does |
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| 122 | ! not lead to the effective stress seen over the whole barotropic loop. |
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| 123 | ! G. Madec : in linear free surface, e3u_a = e3u_n = e3u_0, so systematic use of e3u_a |
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| 124 | IF( ln_drgimp .AND. ln_dynspg_ts ) THEN |
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| 125 | DO jk = 1, jpkm1 ! remove barotropic velocities |
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| 126 | ua(:,:,jk) = ( ua(:,:,jk) - ua_b(:,:) ) * umask(:,:,jk) |
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| 127 | va(:,:,jk) = ( va(:,:,jk) - va_b(:,:) ) * vmask(:,:,jk) |
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| 128 | END DO |
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| 129 | DO jj = 2, jpjm1 ! Add bottom/top stress due to barotropic component only |
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| 130 | DO ji = fs_2, fs_jpim1 ! vector opt. |
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| 131 | iku = mbku(ji,jj) ! ocean bottom level at u- and v-points |
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| 132 | ikv = mbkv(ji,jj) ! (deepest ocean u- and v-points) |
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| 133 | ze3ua = ( 1._wp - r_vvl ) * e3u_n(ji,jj,iku) + r_vvl * e3u_a(ji,jj,iku) |
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| 134 | ze3va = ( 1._wp - r_vvl ) * e3v_n(ji,jj,ikv) + r_vvl * e3v_a(ji,jj,ikv) |
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[9939] | 135 | ua(ji,jj,iku) = ua(ji,jj,iku) + z2dt_2 * ( rCdU_bot(ji+1,jj)+rCdU_bot(ji,jj) ) * ua_b(ji,jj) / ze3ua |
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| 136 | va(ji,jj,ikv) = va(ji,jj,ikv) + z2dt_2 * ( rCdU_bot(ji,jj+1)+rCdU_bot(ji,jj) ) * va_b(ji,jj) / ze3va |
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[9019] | 137 | END DO |
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| 138 | END DO |
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| 139 | IF( ln_isfcav ) THEN ! Ocean cavities (ISF) |
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| 140 | DO jj = 2, jpjm1 |
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| 141 | DO ji = fs_2, fs_jpim1 ! vector opt. |
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| 142 | iku = miku(ji,jj) ! top ocean level at u- and v-points |
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| 143 | ikv = mikv(ji,jj) ! (first wet ocean u- and v-points) |
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| 144 | ze3ua = ( 1._wp - r_vvl ) * e3u_n(ji,jj,iku) + r_vvl * e3u_a(ji,jj,iku) |
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| 145 | ze3va = ( 1._wp - r_vvl ) * e3v_n(ji,jj,ikv) + r_vvl * e3v_a(ji,jj,ikv) |
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[9939] | 146 | ua(ji,jj,iku) = ua(ji,jj,iku) + z2dt_2 * ( rCdU_top(ji+1,jj)+rCdU_top(ji,jj) ) * ua_b(ji,jj) / ze3ua |
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| 147 | va(ji,jj,ikv) = va(ji,jj,ikv) + z2dt_2 * ( rCdU_top(ji+1,jj)+rCdU_top(ji,jj) ) * va_b(ji,jj) / ze3va |
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[9019] | 148 | END DO |
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| 149 | END DO |
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| 150 | END IF |
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| 151 | ENDIF |
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| 152 | ! |
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| 153 | ! !== Vertical diffusion on u ==! |
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| 154 | ! |
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[9939] | 155 | SELECT CASE( nldf_dyn ) !* Matrix construction |
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| 156 | ! |
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| 157 | CASE( np_lap_i ) ! rotated lateral mixing: add its vertical mixing (akzu) |
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[9019] | 158 | DO jk = 1, jpkm1 |
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| 159 | DO jj = 2, jpjm1 |
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| 160 | DO ji = fs_2, fs_jpim1 ! vector opt. |
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| 161 | ze3ua = ( 1._wp - r_vvl ) * e3u_n(ji,jj,jk) + r_vvl * e3u_a(ji,jj,jk) ! after scale factor at T-point |
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[9939] | 162 | zzwi = - rDt * ( 0.5 * ( avm(ji+1,jj,jk ) + avm(ji,jj,jk ) ) + akzu(ji,jj,jk ) ) & |
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| 163 | & / ( ze3ua * e3uw_n(ji,jj,jk ) ) * wumask(ji,jj,jk ) |
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| 164 | zzws = - rDt * ( 0.5 * ( avm(ji+1,jj,jk+1) + avm(ji,jj,jk+1) ) + akzu(ji,jj,jk+1) ) & |
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| 165 | & / ( ze3ua * e3uw_n(ji,jj,jk+1) ) * wumask(ji,jj,jk+1) |
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[9019] | 166 | zwi(ji,jj,jk) = zzwi |
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| 167 | zws(ji,jj,jk) = zzws |
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| 168 | zwd(ji,jj,jk) = 1._wp - zzwi - zzws |
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| 169 | END DO |
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| 170 | END DO |
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| 171 | END DO |
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[9939] | 172 | CASE DEFAULT ! iso-level lateral mixing |
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[9019] | 173 | DO jk = 1, jpkm1 |
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| 174 | DO jj = 2, jpjm1 |
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| 175 | DO ji = fs_2, fs_jpim1 ! vector opt. |
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| 176 | ze3ua = ( 1._wp - r_vvl ) * e3u_n(ji,jj,jk) + r_vvl * e3u_a(ji,jj,jk) ! after scale factor at T-point |
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[9939] | 177 | zzwi = - z2dt_2 * ( avm(ji+1,jj,jk ) + avm(ji,jj,jk ) ) / ( ze3ua * e3uw_n(ji,jj,jk ) ) * wumask(ji,jj,jk ) |
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| 178 | zzws = - z2dt_2 * ( avm(ji+1,jj,jk+1) + avm(ji,jj,jk+1) ) / ( ze3ua * e3uw_n(ji,jj,jk+1) ) * wumask(ji,jj,jk+1) |
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[9019] | 179 | zwi(ji,jj,jk) = zzwi |
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| 180 | zws(ji,jj,jk) = zzws |
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| 181 | zwd(ji,jj,jk) = 1._wp - zzwi - zzws |
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| 182 | END DO |
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| 183 | END DO |
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| 184 | END DO |
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[9490] | 185 | END SELECT |
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[9019] | 186 | ! |
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[9939] | 187 | DO jj = 2, jpjm1 !* Surface boundary conditions |
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| 188 | DO ji = fs_2, fs_jpim1 ! vector opt. |
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[9019] | 189 | zwi(ji,jj,1) = 0._wp |
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| 190 | zwd(ji,jj,1) = 1._wp - zws(ji,jj,1) |
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| 191 | END DO |
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| 192 | END DO |
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| 193 | ! |
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| 194 | ! !== Apply semi-implicit bottom friction ==! |
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| 195 | ! |
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| 196 | ! Only needed for semi-implicit bottom friction setup. The explicit |
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| 197 | ! bottom friction has been included in "u(v)a" which act as the R.H.S |
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| 198 | ! column vector of the tri-diagonal matrix equation |
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| 199 | ! |
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| 200 | IF ( ln_drgimp ) THEN ! implicit bottom friction |
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| 201 | DO jj = 2, jpjm1 |
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| 202 | DO ji = 2, jpim1 |
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| 203 | iku = mbku(ji,jj) ! ocean bottom level at u- and v-points |
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| 204 | ze3ua = ( 1._wp - r_vvl ) * e3u_n(ji,jj,iku) + r_vvl * e3u_a(ji,jj,iku) ! after scale factor at T-point |
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[9939] | 205 | zwd(ji,jj,iku) = zwd(ji,jj,iku) - z2dt_2 * ( rCdU_bot(ji+1,jj)+rCdU_bot(ji,jj) ) / ze3ua |
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[9019] | 206 | END DO |
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| 207 | END DO |
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| 208 | IF ( ln_isfcav ) THEN ! top friction (always implicit) |
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| 209 | DO jj = 2, jpjm1 |
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| 210 | DO ji = 2, jpim1 |
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| 211 | !!gm top Cd is masked (=0 outside cavities) no need of test on mik>=2 ==>> it has been suppressed |
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| 212 | iku = miku(ji,jj) ! ocean top level at u- and v-points |
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| 213 | ze3ua = ( 1._wp - r_vvl ) * e3u_n(ji,jj,iku) + r_vvl * e3u_a(ji,jj,iku) ! after scale factor at T-point |
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[9939] | 214 | zwd(ji,jj,iku) = zwd(ji,jj,iku) - z2dt_2 * ( rCdU_top(ji+1,jj)+rCdU_top(ji,jj) ) / ze3ua |
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[9019] | 215 | END DO |
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| 216 | END DO |
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| 217 | END IF |
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| 218 | ENDIF |
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| 219 | ! |
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| 220 | ! Matrix inversion starting from the first level |
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| 221 | !----------------------------------------------------------------------- |
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| 222 | ! solve m.x = y where m is a tri diagonal matrix ( jpk*jpk ) |
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| 223 | ! |
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| 224 | ! ( zwd1 zws1 0 0 0 )( zwx1 ) ( zwy1 ) |
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| 225 | ! ( zwi2 zwd2 zws2 0 0 )( zwx2 ) ( zwy2 ) |
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| 226 | ! ( 0 zwi3 zwd3 zws3 0 )( zwx3 )=( zwy3 ) |
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| 227 | ! ( ... )( ... ) ( ... ) |
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| 228 | ! ( 0 0 0 zwik zwdk )( zwxk ) ( zwyk ) |
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| 229 | ! |
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| 230 | ! m is decomposed in the product of an upper and a lower triangular matrix |
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| 231 | ! The 3 diagonal terms are in 2d arrays: zwd, zws, zwi |
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| 232 | ! The solution (the after velocity) is in ua |
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| 233 | !----------------------------------------------------------------------- |
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| 234 | ! |
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| 235 | DO jk = 2, jpkm1 !== First recurrence : Dk = Dk - Lk * Uk-1 / Dk-1 (increasing k) == |
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| 236 | DO jj = 2, jpjm1 |
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| 237 | DO ji = fs_2, fs_jpim1 ! vector opt. |
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| 238 | 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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| 239 | END DO |
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| 240 | END DO |
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| 241 | END DO |
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| 242 | ! |
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| 243 | DO jj = 2, jpjm1 !== second recurrence: SOLk = RHSk - Lk / Dk-1 Lk-1 ==! |
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| 244 | DO ji = fs_2, fs_jpim1 ! vector opt. |
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| 245 | ze3ua = ( 1._wp - r_vvl ) * e3u_n(ji,jj,1) + r_vvl * e3u_a(ji,jj,1) |
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[9939] | 246 | ua(ji,jj,1) = ua(ji,jj,1) + z2dt_2 * ( utau_b(ji,jj) + utau(ji,jj) ) / ( ze3ua * rho0 ) * umask(ji,jj,1) |
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[9019] | 247 | END DO |
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| 248 | END DO |
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| 249 | DO jk = 2, jpkm1 |
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| 250 | DO jj = 2, jpjm1 |
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| 251 | DO ji = fs_2, fs_jpim1 |
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| 252 | ua(ji,jj,jk) = ua(ji,jj,jk) - zwi(ji,jj,jk) / zwd(ji,jj,jk-1) * ua(ji,jj,jk-1) |
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| 253 | END DO |
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| 254 | END DO |
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| 255 | END DO |
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| 256 | ! |
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| 257 | DO jj = 2, jpjm1 !== thrid recurrence : SOLk = ( Lk - Uk * Ek+1 ) / Dk ==! |
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| 258 | DO ji = fs_2, fs_jpim1 ! vector opt. |
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| 259 | ua(ji,jj,jpkm1) = ua(ji,jj,jpkm1) / zwd(ji,jj,jpkm1) |
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| 260 | END DO |
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| 261 | END DO |
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| 262 | DO jk = jpk-2, 1, -1 |
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| 263 | DO jj = 2, jpjm1 |
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| 264 | DO ji = fs_2, fs_jpim1 |
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| 265 | ua(ji,jj,jk) = ( ua(ji,jj,jk) - zws(ji,jj,jk) * ua(ji,jj,jk+1) ) / zwd(ji,jj,jk) |
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| 266 | END DO |
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| 267 | END DO |
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| 268 | END DO |
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| 269 | ! |
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| 270 | ! !== Vertical diffusion on v ==! |
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| 271 | ! |
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[9939] | 272 | ! |
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| 273 | SELECT CASE( nldf_dyn ) !* Matrix construction |
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| 274 | CASE( np_lap_i ) ! rotated lateral mixing: add its vertical mixing (akzu) |
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[9019] | 275 | DO jk = 1, jpkm1 |
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| 276 | DO jj = 2, jpjm1 |
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| 277 | DO ji = fs_2, fs_jpim1 ! vector opt. |
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| 278 | ze3va = ( 1._wp - r_vvl ) * e3v_n(ji,jj,jk) + r_vvl * e3v_a(ji,jj,jk) ! after scale factor at T-point |
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[9939] | 279 | zzwi = - rDt * ( 0.5 * ( avm(ji,jj+1,jk ) + avm(ji,jj,jk ) ) + akzv(ji,jj,jk ) ) & |
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| 280 | & / ( ze3va * e3vw_n(ji,jj,jk ) ) * wvmask(ji,jj,jk ) |
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| 281 | zzws = - rDt * ( 0.5 * ( avm(ji,jj+1,jk+1) + avm(ji,jj,jk+1) ) + akzv(ji,jj,jk+1) ) & |
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| 282 | & / ( ze3va * e3vw_n(ji,jj,jk+1) ) * wvmask(ji,jj,jk+1) |
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[9019] | 283 | zwi(ji,jj,jk) = zzwi * wvmask(ji,jj,jk ) |
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| 284 | zws(ji,jj,jk) = zzws * wvmask(ji,jj,jk+1) |
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| 285 | zwd(ji,jj,jk) = 1._wp - zzwi - zzws |
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| 286 | END DO |
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| 287 | END DO |
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| 288 | END DO |
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[9939] | 289 | CASE DEFAULT ! iso-level lateral mixing |
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[9019] | 290 | DO jk = 1, jpkm1 |
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| 291 | DO jj = 2, jpjm1 |
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| 292 | DO ji = fs_2, fs_jpim1 ! vector opt. |
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| 293 | ze3va = ( 1._wp - r_vvl ) * e3v_n(ji,jj,jk) + r_vvl * e3v_a(ji,jj,jk) ! after scale factor at T-point |
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[9939] | 294 | zzwi = - z2dt_2 * ( avm(ji,jj+1,jk ) + avm(ji,jj,jk ) ) / ( ze3va * e3vw_n(ji,jj,jk ) ) * wvmask(ji,jj,jk ) |
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| 295 | zzws = - z2dt_2 * ( avm(ji,jj+1,jk+1) + avm(ji,jj,jk+1) ) / ( ze3va * e3vw_n(ji,jj,jk+1) ) * wvmask(ji,jj,jk+1) |
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[9019] | 296 | zwi(ji,jj,jk) = zzwi * wvmask(ji,jj,jk ) |
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| 297 | zws(ji,jj,jk) = zzws * wvmask(ji,jj,jk+1) |
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| 298 | zwd(ji,jj,jk) = 1._wp - zzwi - zzws |
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| 299 | END DO |
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| 300 | END DO |
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| 301 | END DO |
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[9490] | 302 | END SELECT |
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[9019] | 303 | ! |
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[9939] | 304 | DO jj = 2, jpjm1 !* Surface boundary conditions |
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| 305 | DO ji = fs_2, fs_jpim1 ! vector opt. |
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[9019] | 306 | zwi(ji,jj,1) = 0._wp |
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| 307 | zwd(ji,jj,1) = 1._wp - zws(ji,jj,1) |
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| 308 | END DO |
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| 309 | END DO |
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| 310 | ! !== Apply semi-implicit top/bottom friction ==! |
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| 311 | ! |
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| 312 | ! Only needed for semi-implicit bottom friction setup. The explicit |
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| 313 | ! bottom friction has been included in "u(v)a" which act as the R.H.S |
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| 314 | ! column vector of the tri-diagonal matrix equation |
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| 315 | ! |
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| 316 | IF( ln_drgimp ) THEN |
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| 317 | DO jj = 2, jpjm1 |
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| 318 | DO ji = 2, jpim1 |
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| 319 | ikv = mbkv(ji,jj) ! (deepest ocean u- and v-points) |
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| 320 | ze3va = ( 1._wp - r_vvl ) * e3v_n(ji,jj,ikv) + r_vvl * e3v_a(ji,jj,ikv) ! after scale factor at T-point |
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[9939] | 321 | zwd(ji,jj,ikv) = zwd(ji,jj,ikv) - z2dt_2 * ( rCdU_bot(ji,jj+1)+rCdU_bot(ji,jj) ) / ze3va |
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[9019] | 322 | END DO |
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| 323 | END DO |
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| 324 | IF ( ln_isfcav ) THEN |
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| 325 | DO jj = 2, jpjm1 |
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| 326 | DO ji = 2, jpim1 |
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| 327 | ikv = mikv(ji,jj) ! (first wet ocean u- and v-points) |
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| 328 | ze3va = ( 1._wp - r_vvl ) * e3v_n(ji,jj,ikv) + r_vvl * e3v_a(ji,jj,ikv) ! after scale factor at T-point |
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[9939] | 329 | zwd(ji,jj,iku) = zwd(ji,jj,iku) - z2dt_2 * ( rCdU_top(ji+1,jj)+rCdU_top(ji,jj) ) / ze3va |
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[9019] | 330 | END DO |
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| 331 | END DO |
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| 332 | ENDIF |
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| 333 | ENDIF |
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[456] | 334 | |
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[9019] | 335 | ! Matrix inversion |
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| 336 | !----------------------------------------------------------------------- |
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| 337 | ! solve m.x = y where m is a tri diagonal matrix ( jpk*jpk ) |
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[503] | 338 | ! |
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[9019] | 339 | ! ( zwd1 zws1 0 0 0 )( zwx1 ) ( zwy1 ) |
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| 340 | ! ( zwi2 zwd2 zws2 0 0 )( zwx2 ) ( zwy2 ) |
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| 341 | ! ( 0 zwi3 zwd3 zws3 0 )( zwx3 )=( zwy3 ) |
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| 342 | ! ( ... )( ... ) ( ... ) |
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| 343 | ! ( 0 0 0 zwik zwdk )( zwxk ) ( zwyk ) |
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[503] | 344 | ! |
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[9019] | 345 | ! m is decomposed in the product of an upper and lower triangular matrix |
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| 346 | ! The 3 diagonal terms are in 2d arrays: zwd, zws, zwi |
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| 347 | ! The solution (after velocity) is in 2d array va |
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| 348 | !----------------------------------------------------------------------- |
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| 349 | ! |
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| 350 | DO jk = 2, jpkm1 !== First recurrence : Dk = Dk - Lk * Uk-1 / Dk-1 (increasing k) == |
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| 351 | DO jj = 2, jpjm1 |
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| 352 | DO ji = fs_2, fs_jpim1 ! vector opt. |
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| 353 | 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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| 354 | END DO |
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| 355 | END DO |
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| 356 | END DO |
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| 357 | ! |
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| 358 | DO jj = 2, jpjm1 !== second recurrence: SOLk = RHSk - Lk / Dk-1 Lk-1 ==! |
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| 359 | DO ji = fs_2, fs_jpim1 ! vector opt. |
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| 360 | ze3va = ( 1._wp - r_vvl ) * e3v_n(ji,jj,1) + r_vvl * e3v_a(ji,jj,1) |
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[9939] | 361 | va(ji,jj,1) = va(ji,jj,1) + z2dt_2 * ( vtau_b(ji,jj) + vtau(ji,jj) ) / ( ze3va * rho0 ) * vmask(ji,jj,1) |
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[9019] | 362 | END DO |
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| 363 | END DO |
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| 364 | DO jk = 2, jpkm1 |
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| 365 | DO jj = 2, jpjm1 |
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| 366 | DO ji = fs_2, fs_jpim1 ! vector opt. |
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| 367 | va(ji,jj,jk) = va(ji,jj,jk) - zwi(ji,jj,jk) / zwd(ji,jj,jk-1) * va(ji,jj,jk-1) |
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| 368 | END DO |
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| 369 | END DO |
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| 370 | END DO |
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| 371 | ! |
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| 372 | DO jj = 2, jpjm1 !== third recurrence : SOLk = ( Lk - Uk * SOLk+1 ) / Dk ==! |
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| 373 | DO ji = fs_2, fs_jpim1 ! vector opt. |
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| 374 | va(ji,jj,jpkm1) = va(ji,jj,jpkm1) / zwd(ji,jj,jpkm1) |
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| 375 | END DO |
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| 376 | END DO |
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| 377 | DO jk = jpk-2, 1, -1 |
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| 378 | DO jj = 2, jpjm1 |
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| 379 | DO ji = fs_2, fs_jpim1 |
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| 380 | va(ji,jj,jk) = ( va(ji,jj,jk) - zws(ji,jj,jk) * va(ji,jj,jk+1) ) / zwd(ji,jj,jk) |
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| 381 | END DO |
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| 382 | END DO |
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| 383 | END DO |
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| 384 | ! |
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[9939] | 385 | IF( l_trddyn ) THEN ! save the vertical diffusive trends for further diagnostics |
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| 386 | IF( ln_dynadv_vec .OR. ln_linssh ) THEN ! applied on velocity |
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| 387 | ztrdu(:,:,:) = ( ua(:,:,:) - ub(:,:,:) ) * r1_Dt - ztrdu(:,:,:) |
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| 388 | ztrdv(:,:,:) = ( va(:,:,:) - vb(:,:,:) ) * r1_Dt - ztrdv(:,:,:) |
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| 389 | ELSE ! applied on thickness weighted velocity |
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| 390 | ztrdu(:,:,:) = ( e3u_a(:,:,:)*ua(:,:,:) - e3u_b(:,:,:)*ub(:,:,:) ) / e3u_n(:,:,:) * r1_Dt - ztrdu(:,:,:) |
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| 391 | ztrdv(:,:,:) = ( e3v_a(:,:,:)*va(:,:,:) - e3v_b(:,:,:)*vb(:,:,:) ) / e3v_n(:,:,:) * r1_Dt - ztrdv(:,:,:) |
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| 392 | ENDIF |
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[4990] | 393 | CALL trd_dyn( ztrdu, ztrdv, jpdyn_zdf, kt ) |
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[9019] | 394 | DEALLOCATE( ztrdu, ztrdv ) |
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[456] | 395 | ENDIF |
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| 396 | ! ! print mean trends (used for debugging) |
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| 397 | IF(ln_ctl) CALL prt_ctl( tab3d_1=ua, clinfo1=' zdf - Ua: ', mask1=umask, & |
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[5836] | 398 | & tab3d_2=va, clinfo2= ' Va: ', mask2=vmask, clinfo3='dyn' ) |
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| 399 | ! |
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[9019] | 400 | IF( ln_timing ) CALL timing_stop('dyn_zdf') |
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[503] | 401 | ! |
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[456] | 402 | END SUBROUTINE dyn_zdf |
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| 403 | |
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[9939] | 404 | !!gm currently not used : just for memory to be able to add dissipation trend through vertical mixing |
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| 405 | |
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| 406 | SUBROUTINE zdf_trd( ptrdu, ptrdv ,kt ) |
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| 407 | !!---------------------------------------------------------------------- |
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| 408 | !! *** ROUTINE zdf_trd *** |
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| 409 | !! |
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| 410 | !! ** Purpose : compute the trend due to the vert. momentum diffusion |
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| 411 | !! together with the Leap-Frog time stepping using an |
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| 412 | !! implicit scheme. |
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| 413 | !! |
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| 414 | !! ** Method : - Leap-Frog time stepping on all trends but the vertical mixing |
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| 415 | !! ua = ub + 2*dt * ua vector form or linear free surf. |
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| 416 | !! ua = ( e3u_b*ub + 2*dt * e3u_n*ua ) / e3u_a otherwise |
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| 417 | !! - update the after velocity with the implicit vertical mixing. |
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| 418 | !! This requires to solver the following system: |
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| 419 | !! ua = ua + 1/e3u_a dk+1[ mi(avm) / e3uw_a dk[ua] ] |
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| 420 | !! with the following surface/top/bottom boundary condition: |
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| 421 | !! surface: wind stress input (averaged over kt-1/2 & kt+1/2) |
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| 422 | !! top & bottom : top stress (iceshelf-ocean) & bottom stress (cf zdfdrg.F90) |
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| 423 | !! |
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| 424 | !! ** Action : (ua,va) after velocity |
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| 425 | !!--------------------------------------------------------------------- |
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| 426 | REAL(wp), INTENT(inout), DIMENSION(jpi,jpj,jpk) :: ptrdu, ptrdv ! 3D work arrays use for zdf trends diag |
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| 427 | INTEGER , INTENT(in ) :: kt ! ocean time-step index |
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| 428 | ! |
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| 429 | INTEGER :: ji, jj, jk ! dummy loop indices |
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| 430 | REAL(wp) :: zzz ! local scalar |
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| 431 | REAL(wp) :: zavmu, zavmum1 ! - - |
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| 432 | REAL(wp) :: zavmv, zavmvm1 ! - - |
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| 433 | REAL(wp), DIMENSION(:,:), ALLOCATABLE :: z2d ! - - |
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| 434 | !!--------------------------------------------------------------------- |
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| 435 | ! |
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| 436 | CALL lbc_lnk_multi( ua, 'U', -1., va, 'V', -1. ) ! apply lateral boundary condition on (ua,va) |
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| 437 | ! |
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| 438 | ! |
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| 439 | ! !== momentum trend due to vertical diffusion ==! |
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| 440 | ! |
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| 441 | IF( ln_dynadv_vec .OR. ln_linssh ) THEN ! applied on velocity |
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| 442 | ptrdu(:,:,:) = ( ua(:,:,:) - ub(:,:,:) ) * r1_Dt - ptrdu(:,:,:) |
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| 443 | ptrdv(:,:,:) = ( va(:,:,:) - vb(:,:,:) ) * r1_Dt - ptrdv(:,:,:) |
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| 444 | ELSE ! applied on thickness weighted velocity |
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| 445 | ptrdu(:,:,:) = ( e3u_a(:,:,:)*ua(:,:,:) - e3u_b(:,:,:)*ub(:,:,:) ) / e3u_n(:,:,:) * r1_Dt - ptrdu(:,:,:) |
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| 446 | ptrdv(:,:,:) = ( e3v_a(:,:,:)*va(:,:,:) - e3v_b(:,:,:)*vb(:,:,:) ) / e3v_n(:,:,:) * r1_Dt - ptrdv(:,:,:) |
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| 447 | ENDIF |
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| 448 | CALL trd_dyn( ptrdu, ptrdv, jpdyn_zdf, kt ) |
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| 449 | ! |
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| 450 | ! |
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| 451 | ! !== KE dissipation trend due to vertical diffusion ==! |
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| 452 | ! |
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| 453 | IF( iom_use( 'dispkevfo' ) ) THEN ! ocean kinetic energy dissipation per unit area |
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| 454 | ! ! due to v friction (v=vertical) |
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| 455 | ! ! see NEMO_book appendix C, §C.8 (N.B. here averaged at t-points) |
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| 456 | ! ! Note that formally, in a Leap-Frog environment, the shear**2 should be the product of |
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| 457 | ! ! now by before shears, i.e. the source term of TKE (local positivity is not ensured). |
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| 458 | ! ! Note also that now e3 scale factors are used as after one are not computed ! |
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| 459 | ! |
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[10001] | 460 | ALLOCATE( z2d(jpi,jpj) ) |
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[9939] | 461 | z2d(:,:) = 0._wp |
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| 462 | DO jk = 1, jpkm1 |
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| 463 | DO jj = 2, jpjm1 |
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| 464 | DO ji = 2, jpim1 |
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| 465 | zavmu = 0.5 * ( avm(ji+1,jj,jk) + avm(ji ,jj,jk) ) |
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| 466 | zavmum1 = 0.5 * ( avm(ji ,jj,jk) + avm(ji-1,jj,jk) ) |
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| 467 | zavmv = 0.5 * ( avm(ji,jj+1,jk) + avm(ji,jj ,jk) ) |
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| 468 | zavmvm1 = 0.5 * ( avm(ji,jj ,jk) + avm(ji,jj-1,jk) ) |
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| 469 | |
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| 470 | z2d(ji,jj) = z2d(ji,jj) + ( & |
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| 471 | & zavmu * ( ua(ji ,jj,jk-1) - ua(ji ,jj,jk) )**2 / e3uw_n(ji ,jj,jk) * wumask(ji ,jj,jk) & |
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| 472 | & + zavmum1 * ( ua(ji-1,jj,jk-1) - ua(ji-1,jj,jk) )**2 / e3uw_n(ji-1,jj,jk) * wumask(ji-1,jj,jk) & |
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| 473 | & + zavmv * ( va(ji,jj ,jk-1) - va(ji,jj ,jk) )**2 / e3vw_n(ji,jj ,jk) * wvmask(ji,jj ,jk) & |
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| 474 | & + zavmvm1 * ( va(ji,jj-1,jk-1) - va(ji,jj-1,jk) )**2 / e3vw_n(ji,jj-1,jk) * wvmask(ji,jj-1,jk) & |
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| 475 | & ) |
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| 476 | !!gm --- This trends is in fact properly computed in zdf_sh2 but with a backward shift of one time-step ===>>> use it ? |
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| 477 | !! No since in zdfshé only kz tke (or gls) is used |
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| 478 | !! |
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| 479 | !!gm --- formally, as done below, in a Leap-Frog environment, the shear**2 should be the product of |
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| 480 | !!gm now by before shears, i.e. the source term of TKE (local positivity is not ensured). |
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| 481 | !! CAUTION: requires to compute e3uw_a and e3vw_a !!! |
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| 482 | ! z2d(ji,jj) = z2d(ji,jj) + ( & |
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| 483 | ! & avmu(ji ,jj,jk) * ( un(ji ,jj,jk-1) - un(ji ,jj,jk) ) / e3uw_n(ji ,jj,jk) & |
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| 484 | ! & * ( ua(ji ,jj,jk-1) - ua(ji ,jj,jk) ) / e3uw_a(ji ,jj,jk) * wumask(ji ,jj,jk) & |
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| 485 | ! & + avmu(ji-1,jj,jk) * ( un(ji-1,jj,jk-1) - un(ji-1,jj,jk) ) / e3uw_n(ji-1,jj,jk) & |
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| 486 | ! & ( ua(ji-1,jj,jk-1) - ua(ji-1,jj,jk) ) / e3uw_a(ji-1,jj,jk) * wumask(ji-1,jj,jk) & |
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| 487 | ! & + avmv(ji,jj ,jk) * ( vn(ji,jj ,jk-1) - vn(ji,jj ,jk) ) / e3vw_n(ji,jj ,jk) & |
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| 488 | ! & ( va(ji,jj ,jk-1) - va(ji,jj ,jk) ) / e3vw_a(ji,jj ,jk) * wvmask(ji,jj ,jk) & |
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| 489 | ! & + avmv(ji,jj-1,jk) * ( vn(ji,jj-1,jk-1) - vn(ji,jj-1,jk) ) / e3vw_n(ji,jj-1,jk) & |
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| 490 | ! & ( va(ji,jj-1,jk-1) - va(ji,jj-1,jk) ) / e3vw_a(ji,jj-1,jk) * wvmask(ji,jj-1,jk) & |
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| 491 | ! & ) |
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| 492 | !!gm end |
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| 493 | END DO |
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| 494 | END DO |
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| 495 | END DO |
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| 496 | zzz= - 0.5_wp* rho0 ! caution sign minus here |
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| 497 | z2d(:,:) = zzz * z2d(:,:) |
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| 498 | CALL lbc_lnk( z2d,'T', 1. ) |
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| 499 | CALL iom_put( 'dispkevfo', z2d ) |
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[10001] | 500 | DEALLOCATE( z2d ) |
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[9939] | 501 | ENDIF |
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| 502 | ! |
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| 503 | END SUBROUTINE zdf_trd |
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| 504 | |
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| 505 | !!gm end not used |
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| 506 | |
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[456] | 507 | !!============================================================================== |
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| 508 | END MODULE dynzdf |
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