[3] | 1 | MODULE dynzdf_imp |
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| 2 | !!============================================================================== |
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| 3 | !! *** MODULE dynzdf_imp *** |
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| 4 | !! Ocean dynamics: vertical component(s) of the momentum mixing trend |
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| 5 | !!============================================================================== |
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[2528] | 6 | !! History : OPA ! 1990-10 (B. Blanke) Original code |
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| 7 | !! 8.0 ! 1997-05 (G. Madec) vertical component of isopycnal |
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| 8 | !! NEMO 1.0 ! 2002-08 (G. Madec) F90: Free form and module |
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| 9 | !! 3.3 ! 2010-04 (M. Leclair, G. Madec) Forcing averaged over 2 time steps |
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[503] | 10 | !!---------------------------------------------------------------------- |
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[3] | 11 | |
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| 12 | !!---------------------------------------------------------------------- |
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| 13 | !! dyn_zdf_imp : update the momentum trend with the vertical diffu- |
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| 14 | !! sion using a implicit time-stepping. |
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| 15 | !!---------------------------------------------------------------------- |
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| 16 | USE oce ! ocean dynamics and tracers |
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| 17 | USE dom_oce ! ocean space and time domain |
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[888] | 18 | USE sbc_oce ! surface boundary condition: ocean |
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| 19 | USE zdf_oce ! ocean vertical physics |
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[719] | 20 | USE phycst ! physical constants |
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[3] | 21 | USE in_out_manager ! I/O manager |
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[2636] | 22 | USE lib_mpp ! MPP library |
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[3] | 23 | |
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| 24 | IMPLICIT NONE |
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| 25 | PRIVATE |
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| 26 | |
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[2528] | 27 | PUBLIC dyn_zdf_imp ! called by step.F90 |
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[3] | 28 | |
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| 29 | !! * Substitutions |
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| 30 | # include "domzgr_substitute.h90" |
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| 31 | # include "vectopt_loop_substitute.h90" |
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| 32 | !!---------------------------------------------------------------------- |
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[2528] | 33 | !! NEMO/OPA 3.3 , NEMO Consortium (2010) |
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[888] | 34 | !! $Id$ |
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[2528] | 35 | !! Software governed by the CeCILL licence (NEMOGCM/NEMO_CeCILL.txt) |
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[3] | 36 | !!---------------------------------------------------------------------- |
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| 37 | CONTAINS |
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| 38 | |
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[503] | 39 | SUBROUTINE dyn_zdf_imp( kt, p2dt ) |
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[3] | 40 | !!---------------------------------------------------------------------- |
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| 41 | !! *** ROUTINE dyn_zdf_imp *** |
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| 42 | !! |
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| 43 | !! ** Purpose : Compute the trend due to the vert. momentum diffusion |
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| 44 | !! and the surface forcing, and add it to the general trend of |
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| 45 | !! the momentum equations. |
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| 46 | !! |
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| 47 | !! ** Method : The vertical momentum mixing trend is given by : |
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| 48 | !! dz( avmu dz(u) ) = 1/e3u dk+1( avmu/e3uw dk(ua) ) |
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| 49 | !! backward time stepping |
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[2528] | 50 | !! Surface boundary conditions: wind stress input (averaged over kt-1/2 & kt+1/2) |
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[3] | 51 | !! Bottom boundary conditions : bottom stress (cf zdfbfr.F) |
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| 52 | !! Add this trend to the general trend ua : |
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| 53 | !! ua = ua + dz( avmu dz(u) ) |
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| 54 | !! |
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[2528] | 55 | !! ** Action : - Update (ua,va) arrays with the after vertical diffusive mixing trend. |
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[3] | 56 | !!--------------------------------------------------------------------- |
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[2528] | 57 | USE oce, ONLY : zwd => ta ! use ta as workspace |
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| 58 | USE oce, ONLY : zws => sa ! use sa as workspace |
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[2633] | 59 | USE wrk_nemo, ONLY: wrk_in_use, wrk_not_released |
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[2590] | 60 | USE wrk_nemo, ONLY: zwi => wrk_3d_3 ! workspace |
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[2528] | 61 | !! |
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| 62 | INTEGER , INTENT( in ) :: kt ! ocean time-step index |
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| 63 | REAL(wp), INTENT( in ) :: p2dt ! vertical profile of tracer time-step |
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| 64 | !! |
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| 65 | INTEGER :: ji, jj, jk ! dummy loop indices |
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| 66 | REAL(wp) :: z1_p2dt, zcoef ! temporary scalars |
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| 67 | REAL(wp) :: zzwi, zzws, zrhs ! temporary scalars |
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[3] | 68 | !!---------------------------------------------------------------------- |
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| 69 | |
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[2633] | 70 | IF(wrk_in_use(3, 3))THEN |
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[2590] | 71 | CALL ctl_stop('dyn_zdf_imp : requested workspace array unavailable.') |
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| 72 | RETURN |
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| 73 | END IF |
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| 74 | |
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[3] | 75 | IF( kt == nit000 ) THEN |
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| 76 | IF(lwp) WRITE(numout,*) |
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| 77 | IF(lwp) WRITE(numout,*) 'dyn_zdf_imp : vertical momentum diffusion implicit operator' |
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| 78 | IF(lwp) WRITE(numout,*) '~~~~~~~~~~~ ' |
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| 79 | ENDIF |
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| 80 | |
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| 81 | ! 0. Local constant initialization |
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| 82 | ! -------------------------------- |
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[2528] | 83 | z1_p2dt = 1._wp / p2dt ! inverse of the timestep |
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[455] | 84 | |
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[3] | 85 | ! 1. Vertical diffusion on u |
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| 86 | ! --------------------------- |
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| 87 | ! Matrix and second member construction |
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[1662] | 88 | ! bottom boundary condition: both zwi and zws must be masked as avmu can take |
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[3] | 89 | ! non zero value at the ocean bottom depending on the bottom friction |
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[1662] | 90 | ! used but the bottom velocities have already been updated with the bottom |
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| 91 | ! friction velocity in dyn_bfr using values from the previous timestep. There |
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| 92 | ! is no need to include these in the implicit calculation. |
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[2528] | 93 | ! |
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| 94 | DO jk = 1, jpkm1 ! Matrix |
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[3] | 95 | DO jj = 2, jpjm1 |
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| 96 | DO ji = fs_2, fs_jpim1 ! vector opt. |
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[503] | 97 | zcoef = - p2dt / fse3u(ji,jj,jk) |
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[2528] | 98 | zzwi = zcoef * avmu (ji,jj,jk ) / fse3uw(ji,jj,jk ) |
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| 99 | zwi(ji,jj,jk) = zzwi * umask(ji,jj,jk) |
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| 100 | zzws = zcoef * avmu (ji,jj,jk+1) / fse3uw(ji,jj,jk+1) |
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| 101 | zws(ji,jj,jk) = zzws * umask(ji,jj,jk+1) |
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| 102 | zwd(ji,jj,jk) = 1._wp - zwi(ji,jj,jk) - zzws |
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[3] | 103 | END DO |
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| 104 | END DO |
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| 105 | END DO |
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[2528] | 106 | DO jj = 2, jpjm1 ! Surface boudary conditions |
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[3] | 107 | DO ji = fs_2, fs_jpim1 ! vector opt. |
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[2528] | 108 | zwi(ji,jj,1) = 0._wp |
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| 109 | zwd(ji,jj,1) = 1._wp - zws(ji,jj,1) |
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[3] | 110 | END DO |
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| 111 | END DO |
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| 112 | |
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| 113 | ! Matrix inversion starting from the first level |
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| 114 | !----------------------------------------------------------------------- |
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| 115 | ! solve m.x = y where m is a tri diagonal matrix ( jpk*jpk ) |
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| 116 | ! |
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| 117 | ! ( zwd1 zws1 0 0 0 )( zwx1 ) ( zwy1 ) |
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| 118 | ! ( zwi2 zwd2 zws2 0 0 )( zwx2 ) ( zwy2 ) |
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| 119 | ! ( 0 zwi3 zwd3 zws3 0 )( zwx3 )=( zwy3 ) |
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| 120 | ! ( ... )( ... ) ( ... ) |
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| 121 | ! ( 0 0 0 zwik zwdk )( zwxk ) ( zwyk ) |
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| 122 | ! |
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| 123 | ! m is decomposed in the product of an upper and a lower triangular matrix |
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| 124 | ! The 3 diagonal terms are in 2d arrays: zwd, zws, zwi |
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| 125 | ! The solution (the after velocity) is in ua |
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| 126 | !----------------------------------------------------------------------- |
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[2528] | 127 | ! |
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| 128 | DO jk = 2, jpkm1 !== First recurrence : Dk = Dk - Lk * Uk-1 / Dk-1 (increasing k) == |
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[3] | 129 | DO jj = 2, jpjm1 |
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| 130 | DO ji = fs_2, fs_jpim1 ! vector opt. |
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| 131 | 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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| 132 | END DO |
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| 133 | END DO |
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| 134 | END DO |
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[2528] | 135 | ! |
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| 136 | DO jj = 2, jpjm1 !== second recurrence: SOLk = RHSk - Lk / Dk-1 Lk-1 == |
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[3] | 137 | DO ji = fs_2, fs_jpim1 ! vector opt. |
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[2528] | 138 | ua(ji,jj,1) = ub(ji,jj,1) + p2dt * ( ua(ji,jj,1) + 0.5_wp * ( utau_b(ji,jj) + utau(ji,jj) ) & |
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| 139 | & / ( fse3u(ji,jj,1) * rau0 ) ) |
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[3] | 140 | END DO |
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| 141 | END DO |
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| 142 | DO jk = 2, jpkm1 |
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| 143 | DO jj = 2, jpjm1 |
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| 144 | DO ji = fs_2, fs_jpim1 ! vector opt. |
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[503] | 145 | zrhs = ub(ji,jj,jk) + p2dt * ua(ji,jj,jk) ! zrhs=right hand side |
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[3] | 146 | ua(ji,jj,jk) = zrhs - zwi(ji,jj,jk) / zwd(ji,jj,jk-1) * ua(ji,jj,jk-1) |
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| 147 | END DO |
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| 148 | END DO |
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| 149 | END DO |
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[2528] | 150 | ! |
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| 151 | DO jj = 2, jpjm1 !== thrid recurrence : SOLk = ( Lk - Uk * Ek+1 ) / Dk == |
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[3] | 152 | DO ji = fs_2, fs_jpim1 ! vector opt. |
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| 153 | ua(ji,jj,jpkm1) = ua(ji,jj,jpkm1) / zwd(ji,jj,jpkm1) |
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| 154 | END DO |
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| 155 | END DO |
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| 156 | DO jk = jpk-2, 1, -1 |
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| 157 | DO jj = 2, jpjm1 |
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| 158 | DO ji = fs_2, fs_jpim1 ! vector opt. |
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[2528] | 159 | 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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[3] | 160 | END DO |
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| 161 | END DO |
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| 162 | END DO |
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| 163 | |
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| 164 | ! Normalization to obtain the general momentum trend ua |
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| 165 | DO jk = 1, jpkm1 |
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| 166 | DO jj = 2, jpjm1 |
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| 167 | DO ji = fs_2, fs_jpim1 ! vector opt. |
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[2528] | 168 | ua(ji,jj,jk) = ( ua(ji,jj,jk) - ub(ji,jj,jk) ) * z1_p2dt |
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[3] | 169 | END DO |
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| 170 | END DO |
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| 171 | END DO |
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| 172 | |
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| 173 | |
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| 174 | ! 2. Vertical diffusion on v |
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| 175 | ! --------------------------- |
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| 176 | ! Matrix and second member construction |
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[1662] | 177 | ! bottom boundary condition: both zwi and zws must be masked as avmv can take |
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[3] | 178 | ! non zero value at the ocean bottom depending on the bottom friction |
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[1662] | 179 | ! used but the bottom velocities have already been updated with the bottom |
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| 180 | ! friction velocity in dyn_bfr using values from the previous timestep. There |
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| 181 | ! is no need to include these in the implicit calculation. |
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[2528] | 182 | ! |
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| 183 | DO jk = 1, jpkm1 ! Matrix |
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[3] | 184 | DO jj = 2, jpjm1 |
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| 185 | DO ji = fs_2, fs_jpim1 ! vector opt. |
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[503] | 186 | zcoef = -p2dt / fse3v(ji,jj,jk) |
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[2528] | 187 | zzwi = zcoef * avmv (ji,jj,jk ) / fse3vw(ji,jj,jk ) |
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[1662] | 188 | zwi(ji,jj,jk) = zzwi * vmask(ji,jj,jk) |
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[2528] | 189 | zzws = zcoef * avmv (ji,jj,jk+1) / fse3vw(ji,jj,jk+1) |
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[3] | 190 | zws(ji,jj,jk) = zzws * vmask(ji,jj,jk+1) |
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[2528] | 191 | zwd(ji,jj,jk) = 1._wp - zwi(ji,jj,jk) - zzws |
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[3] | 192 | END DO |
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| 193 | END DO |
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| 194 | END DO |
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[2528] | 195 | DO jj = 2, jpjm1 ! Surface boudary conditions |
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[3] | 196 | DO ji = fs_2, fs_jpim1 ! vector opt. |
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[2528] | 197 | zwi(ji,jj,1) = 0._wp |
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| 198 | zwd(ji,jj,1) = 1._wp - zws(ji,jj,1) |
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[3] | 199 | END DO |
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| 200 | END DO |
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| 201 | |
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| 202 | ! Matrix inversion |
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| 203 | !----------------------------------------------------------------------- |
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| 204 | ! solve m.x = y where m is a tri diagonal matrix ( jpk*jpk ) |
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| 205 | ! |
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| 206 | ! ( zwd1 zws1 0 0 0 )( zwx1 ) ( zwy1 ) |
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| 207 | ! ( zwi2 zwd2 zws2 0 0 )( zwx2 ) ( zwy2 ) |
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| 208 | ! ( 0 zwi3 zwd3 zws3 0 )( zwx3 )=( zwy3 ) |
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| 209 | ! ( ... )( ... ) ( ... ) |
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| 210 | ! ( 0 0 0 zwik zwdk )( zwxk ) ( zwyk ) |
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| 211 | ! |
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[2528] | 212 | ! m is decomposed in the product of an upper and lower triangular matrix |
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[3] | 213 | ! The 3 diagonal terms are in 2d arrays: zwd, zws, zwi |
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| 214 | ! The solution (after velocity) is in 2d array va |
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| 215 | !----------------------------------------------------------------------- |
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[2528] | 216 | ! |
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| 217 | DO jk = 2, jpkm1 !== First recurrence : Dk = Dk - Lk * Uk-1 / Dk-1 (increasing k) == |
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[3] | 218 | DO jj = 2, jpjm1 |
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| 219 | DO ji = fs_2, fs_jpim1 ! vector opt. |
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| 220 | 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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| 221 | END DO |
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| 222 | END DO |
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| 223 | END DO |
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[2528] | 224 | ! |
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| 225 | DO jj = 2, jpjm1 !== second recurrence: SOLk = RHSk - Lk / Dk-1 Lk-1 == |
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[3] | 226 | DO ji = fs_2, fs_jpim1 ! vector opt. |
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[2528] | 227 | va(ji,jj,1) = vb(ji,jj,1) + p2dt * ( va(ji,jj,1) + 0.5_wp * ( vtau_b(ji,jj) + vtau(ji,jj) ) & |
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| 228 | & / ( fse3v(ji,jj,1) * rau0 ) ) |
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[3] | 229 | END DO |
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| 230 | END DO |
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| 231 | DO jk = 2, jpkm1 |
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| 232 | DO jj = 2, jpjm1 |
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| 233 | DO ji = fs_2, fs_jpim1 ! vector opt. |
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[503] | 234 | zrhs = vb(ji,jj,jk) + p2dt * va(ji,jj,jk) ! zrhs=right hand side |
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[3] | 235 | va(ji,jj,jk) = zrhs - zwi(ji,jj,jk) / zwd(ji,jj,jk-1) * va(ji,jj,jk-1) |
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| 236 | END DO |
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| 237 | END DO |
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| 238 | END DO |
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[2528] | 239 | ! |
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| 240 | DO jj = 2, jpjm1 !== thrid recurrence : SOLk = ( Lk - Uk * SOLk+1 ) / Dk == |
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[3] | 241 | DO ji = fs_2, fs_jpim1 ! vector opt. |
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| 242 | va(ji,jj,jpkm1) = va(ji,jj,jpkm1) / zwd(ji,jj,jpkm1) |
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| 243 | END DO |
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| 244 | END DO |
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| 245 | DO jk = jpk-2, 1, -1 |
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| 246 | DO jj = 2, jpjm1 |
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| 247 | DO ji = fs_2, fs_jpim1 ! vector opt. |
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[2528] | 248 | 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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[3] | 249 | END DO |
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| 250 | END DO |
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| 251 | END DO |
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| 252 | |
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| 253 | ! Normalization to obtain the general momentum trend va |
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| 254 | DO jk = 1, jpkm1 |
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| 255 | DO jj = 2, jpjm1 |
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| 256 | DO ji = fs_2, fs_jpim1 ! vector opt. |
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[2528] | 257 | va(ji,jj,jk) = ( va(ji,jj,jk) - vb(ji,jj,jk) ) * z1_p2dt |
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[3] | 258 | END DO |
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| 259 | END DO |
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| 260 | END DO |
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[2528] | 261 | ! |
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[2633] | 262 | IF(wrk_not_released(3, 3))THEN |
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[2590] | 263 | CALL ctl_stop('dyn_zdf_imp : failed to release workspace array.') |
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| 264 | END IF |
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| 265 | ! |
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[3] | 266 | END SUBROUTINE dyn_zdf_imp |
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| 267 | |
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| 268 | !!============================================================================== |
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| 269 | END MODULE dynzdf_imp |
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