[3] | 1 | MODULE dynzdf_imp |
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[2715] | 2 | !!====================================================================== |
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[3] | 3 | !! *** MODULE dynzdf_imp *** |
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| 4 | !! Ocean dynamics: vertical component(s) of the momentum mixing trend |
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[2715] | 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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[2715] | 8 | !! NEMO 0.5 ! 2002-08 (G. Madec) F90: Free form and module |
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[2528] | 9 | !! 3.3 ! 2010-04 (M. Leclair, G. Madec) Forcing averaged over 2 time steps |
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[3259] | 10 | !! 3.4 ! 2012-01 (H. Liu) Semi-implicit bottom friction |
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[503] | 11 | !!---------------------------------------------------------------------- |
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[3] | 12 | |
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| 13 | !!---------------------------------------------------------------------- |
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[2715] | 14 | !! dyn_zdf_imp : update the momentum trend with the vertical diffusion using a implicit time-stepping |
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[3] | 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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[2715] | 22 | USE lib_mpp ! MPP library |
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[3259] | 23 | USE zdfbfr ! Bottom friction setup |
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[3186] | 24 | USE wrk_nemo ! Memory Allocation |
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[3161] | 25 | USE timing ! Timing |
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[3] | 26 | |
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| 27 | IMPLICIT NONE |
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| 28 | PRIVATE |
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| 29 | |
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[2528] | 30 | PUBLIC dyn_zdf_imp ! called by step.F90 |
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[3] | 31 | |
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| 32 | !! * Substitutions |
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| 33 | # include "domzgr_substitute.h90" |
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| 34 | # include "vectopt_loop_substitute.h90" |
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| 35 | !!---------------------------------------------------------------------- |
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[2528] | 36 | !! NEMO/OPA 3.3 , NEMO Consortium (2010) |
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[888] | 37 | !! $Id$ |
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[2528] | 38 | !! Software governed by the CeCILL licence (NEMOGCM/NEMO_CeCILL.txt) |
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[3] | 39 | !!---------------------------------------------------------------------- |
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| 40 | CONTAINS |
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| 41 | |
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[503] | 42 | SUBROUTINE dyn_zdf_imp( kt, p2dt ) |
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[3] | 43 | !!---------------------------------------------------------------------- |
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| 44 | !! *** ROUTINE dyn_zdf_imp *** |
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| 45 | !! |
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| 46 | !! ** Purpose : Compute the trend due to the vert. momentum diffusion |
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| 47 | !! and the surface forcing, and add it to the general trend of |
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| 48 | !! the momentum equations. |
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| 49 | !! |
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| 50 | !! ** Method : The vertical momentum mixing trend is given by : |
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| 51 | !! dz( avmu dz(u) ) = 1/e3u dk+1( avmu/e3uw dk(ua) ) |
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| 52 | !! backward time stepping |
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[2528] | 53 | !! Surface boundary conditions: wind stress input (averaged over kt-1/2 & kt+1/2) |
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[3] | 54 | !! Bottom boundary conditions : bottom stress (cf zdfbfr.F) |
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| 55 | !! Add this trend to the general trend ua : |
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| 56 | !! ua = ua + dz( avmu dz(u) ) |
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| 57 | !! |
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[2528] | 58 | !! ** Action : - Update (ua,va) arrays with the after vertical diffusive mixing trend. |
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[3] | 59 | !!--------------------------------------------------------------------- |
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[3161] | 60 | INTEGER , INTENT(in) :: kt ! ocean time-step index |
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[2715] | 61 | REAL(wp), INTENT(in) :: p2dt ! vertical profile of tracer time-step |
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[2528] | 62 | !! |
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[3259] | 63 | INTEGER :: ji, jj, jk ! dummy loop indices |
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| 64 | INTEGER :: ikbu, ikbv ! local integers |
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| 65 | REAL(wp) :: z1_p2dt, zcoef, zzwi, zzws, zrhs ! local scalars |
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| 66 | !!---------------------------------------------------------------------- |
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[3116] | 67 | |
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[3285] | 68 | REAL(wp), POINTER, DIMENSION(:,:,:) :: zwi, zwd, zws |
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| 69 | REAL(wp), POINTER, DIMENSION(:,:) :: zavmu, zavmv |
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[3] | 70 | !!---------------------------------------------------------------------- |
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[2977] | 71 | ! |
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[3161] | 72 | IF( nn_timing == 1 ) CALL timing_start('dyn_zdf_imp') |
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| 73 | ! |
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[3285] | 74 | CALL wrk_alloc( jpi,jpj,jpk, zwi, zwd, zws ) |
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| 75 | CALL wrk_alloc( jpi,jpj, zavmu, zavmv ) |
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[3161] | 76 | ! |
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[3] | 77 | IF( kt == nit000 ) THEN |
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| 78 | IF(lwp) WRITE(numout,*) |
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| 79 | IF(lwp) WRITE(numout,*) 'dyn_zdf_imp : vertical momentum diffusion implicit operator' |
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| 80 | IF(lwp) WRITE(numout,*) '~~~~~~~~~~~ ' |
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| 81 | ENDIF |
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| 82 | |
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| 83 | ! 0. Local constant initialization |
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| 84 | ! -------------------------------- |
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[2528] | 85 | z1_p2dt = 1._wp / p2dt ! inverse of the timestep |
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[455] | 86 | |
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[3259] | 87 | ! 1. Apply semi-implicit bottom friction |
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| 88 | ! -------------------------------------- |
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| 89 | ! Only needed for semi-implicit bottom friction setup. The explicit |
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| 90 | ! bottom friction has been included in "u(v)a" which act as the R.H.S |
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| 91 | ! column vector of the tri-diagonal matrix equation |
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| 92 | ! |
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[3279] | 93 | |
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[3259] | 94 | IF( ln_bfrimp ) THEN |
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| 95 | # if defined key_vectopt_loop |
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| 96 | DO jj = 1, 1 |
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| 97 | DO ji = jpi+2, jpij-jpi-1 ! vector opt. (forced unrolling) |
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| 98 | # else |
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| 99 | DO jj = 2, jpjm1 |
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| 100 | DO ji = 2, jpim1 |
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| 101 | # endif |
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| 102 | ikbu = mbku(ji,jj) ! ocean bottom level at u- and v-points |
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| 103 | ikbv = mbkv(ji,jj) ! (deepest ocean u- and v-points) |
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[3285] | 104 | zavmu(ji,jj) = avmu(ji,jj,ikbu+1) |
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| 105 | zavmv(ji,jj) = avmv(ji,jj,ikbv+1) |
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| 106 | avmu(ji,jj,ikbu+1) = -bfrua(ji,jj) * fse3uw(ji,jj,ikbu+1) |
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| 107 | avmv(ji,jj,ikbv+1) = -bfrva(ji,jj) * fse3vw(ji,jj,ikbv+1) |
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[3259] | 108 | END DO |
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| 109 | END DO |
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| 110 | ENDIF |
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[3116] | 111 | |
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[3259] | 112 | ! 2. Vertical diffusion on u |
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[3] | 113 | ! --------------------------- |
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| 114 | ! Matrix and second member construction |
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[3259] | 115 | ! bottom boundary condition: both zwi and zws must be masked as avmu can take |
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| 116 | ! non zero value at the ocean bottom depending on the bottom friction used. |
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| 117 | ! |
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| 118 | DO jk = 1, jpkm1 ! Matrix |
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| 119 | DO jj = 2, jpjm1 |
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| 120 | DO ji = fs_2, fs_jpim1 ! vector opt. |
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[503] | 121 | zcoef = - p2dt / fse3u(ji,jj,jk) |
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[3285] | 122 | zzwi = zcoef * avmu (ji,jj,jk ) / fse3uw(ji,jj,jk ) |
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[3259] | 123 | zwi(ji,jj,jk) = zzwi * umask(ji,jj,jk) |
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[3285] | 124 | zzws = zcoef * avmu (ji,jj,jk+1) / fse3uw(ji,jj,jk+1) |
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[3259] | 125 | zws(ji,jj,jk) = zzws * umask(ji,jj,jk+1) |
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| 126 | zwd(ji,jj,jk) = 1._wp - zwi(ji,jj,jk) - zzws |
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[3] | 127 | END DO |
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[3259] | 128 | END DO |
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| 129 | END DO |
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| 130 | DO jj = 2, jpjm1 ! Surface boudary conditions |
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| 131 | DO ji = fs_2, fs_jpim1 ! vector opt. |
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[2528] | 132 | zwi(ji,jj,1) = 0._wp |
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| 133 | zwd(ji,jj,1) = 1._wp - zws(ji,jj,1) |
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[3259] | 134 | END DO |
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| 135 | END DO |
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[3] | 136 | |
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| 137 | ! Matrix inversion starting from the first level |
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| 138 | !----------------------------------------------------------------------- |
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| 139 | ! solve m.x = y where m is a tri diagonal matrix ( jpk*jpk ) |
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| 140 | ! |
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| 141 | ! ( zwd1 zws1 0 0 0 )( zwx1 ) ( zwy1 ) |
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| 142 | ! ( zwi2 zwd2 zws2 0 0 )( zwx2 ) ( zwy2 ) |
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| 143 | ! ( 0 zwi3 zwd3 zws3 0 )( zwx3 )=( zwy3 ) |
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| 144 | ! ( ... )( ... ) ( ... ) |
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| 145 | ! ( 0 0 0 zwik zwdk )( zwxk ) ( zwyk ) |
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| 146 | ! |
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| 147 | ! m is decomposed in the product of an upper and a lower triangular matrix |
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| 148 | ! The 3 diagonal terms are in 2d arrays: zwd, zws, zwi |
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| 149 | ! The solution (the after velocity) is in ua |
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| 150 | !----------------------------------------------------------------------- |
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[3259] | 151 | ! |
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| 152 | DO jk = 2, jpkm1 !== First recurrence : Dk = Dk - Lk * Uk-1 / Dk-1 (increasing k) == |
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| 153 | DO jj = 2, jpjm1 |
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| 154 | DO ji = fs_2, fs_jpim1 ! vector opt. |
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[3] | 155 | 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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| 156 | END DO |
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[3259] | 157 | END DO |
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| 158 | END DO |
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| 159 | ! |
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| 160 | DO jj = 2, jpjm1 !== second recurrence: SOLk = RHSk - Lk / Dk-1 Lk-1 == |
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| 161 | DO ji = fs_2, fs_jpim1 ! vector opt. |
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| 162 | 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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| 163 | & / ( fse3u(ji,jj,1) * rau0 ) ) |
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| 164 | END DO |
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| 165 | END DO |
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| 166 | DO jk = 2, 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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[503] | 169 | zrhs = ub(ji,jj,jk) + p2dt * ua(ji,jj,jk) ! zrhs=right hand side |
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[3] | 170 | ua(ji,jj,jk) = zrhs - zwi(ji,jj,jk) / zwd(ji,jj,jk-1) * ua(ji,jj,jk-1) |
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| 171 | END DO |
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[3259] | 172 | END DO |
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| 173 | END DO |
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| 174 | ! |
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| 175 | DO jj = 2, jpjm1 !== thrid recurrence : SOLk = ( Lk - Uk * Ek+1 ) / Dk == |
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| 176 | DO ji = fs_2, fs_jpim1 ! vector opt. |
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| 177 | ua(ji,jj,jpkm1) = ua(ji,jj,jpkm1) / zwd(ji,jj,jpkm1) |
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| 178 | END DO |
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| 179 | END DO |
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| 180 | DO jk = jpk-2, 1, -1 |
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| 181 | DO jj = 2, jpjm1 |
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| 182 | DO ji = fs_2, fs_jpim1 ! vector opt. |
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| 183 | 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] | 184 | END DO |
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| 185 | END DO |
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| 186 | END DO |
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| 187 | |
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| 188 | ! Normalization to obtain the general momentum trend ua |
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| 189 | DO jk = 1, jpkm1 |
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| 190 | DO jj = 2, jpjm1 |
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| 191 | DO ji = fs_2, fs_jpim1 ! vector opt. |
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[2528] | 192 | ua(ji,jj,jk) = ( ua(ji,jj,jk) - ub(ji,jj,jk) ) * z1_p2dt |
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[3] | 193 | END DO |
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| 194 | END DO |
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| 195 | END DO |
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| 196 | |
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| 197 | |
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[3259] | 198 | ! 3. Vertical diffusion on v |
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[3] | 199 | ! --------------------------- |
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[3259] | 200 | ! Matrix and second member construction |
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| 201 | ! bottom boundary condition: both zwi and zws must be masked as avmv can take |
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| 202 | ! non zero value at the ocean bottom depending on the bottom friction used |
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| 203 | ! |
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| 204 | DO jk = 1, jpkm1 ! Matrix |
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[3] | 205 | DO jj = 2, jpjm1 |
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[3259] | 206 | DO ji = fs_2, fs_jpim1 ! vector opt. |
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[503] | 207 | zcoef = -p2dt / fse3v(ji,jj,jk) |
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[3285] | 208 | zzwi = zcoef * avmv (ji,jj,jk ) / fse3vw(ji,jj,jk ) |
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[3259] | 209 | zwi(ji,jj,jk) = zzwi * vmask(ji,jj,jk) |
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[3285] | 210 | zzws = zcoef * avmv (ji,jj,jk+1) / fse3vw(ji,jj,jk+1) |
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[3259] | 211 | zws(ji,jj,jk) = zzws * vmask(ji,jj,jk+1) |
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| 212 | zwd(ji,jj,jk) = 1._wp - zwi(ji,jj,jk) - zzws |
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[3] | 213 | END DO |
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[3259] | 214 | END DO |
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| 215 | END DO |
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| 216 | DO jj = 2, jpjm1 ! Surface boudary conditions |
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| 217 | DO ji = fs_2, fs_jpim1 ! vector opt. |
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[2528] | 218 | zwi(ji,jj,1) = 0._wp |
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| 219 | zwd(ji,jj,1) = 1._wp - zws(ji,jj,1) |
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[3259] | 220 | END DO |
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| 221 | END DO |
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[3] | 222 | |
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| 223 | ! Matrix inversion |
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| 224 | !----------------------------------------------------------------------- |
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| 225 | ! solve m.x = y where m is a tri diagonal matrix ( jpk*jpk ) |
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| 226 | ! |
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| 227 | ! ( zwd1 zws1 0 0 0 )( zwx1 ) ( zwy1 ) |
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| 228 | ! ( zwi2 zwd2 zws2 0 0 )( zwx2 ) ( zwy2 ) |
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| 229 | ! ( 0 zwi3 zwd3 zws3 0 )( zwx3 )=( zwy3 ) |
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| 230 | ! ( ... )( ... ) ( ... ) |
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| 231 | ! ( 0 0 0 zwik zwdk )( zwxk ) ( zwyk ) |
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| 232 | ! |
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[3259] | 233 | ! m is decomposed in the product of an upper and lower triangular matrix |
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[3] | 234 | ! The 3 diagonal terms are in 2d arrays: zwd, zws, zwi |
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| 235 | ! The solution (after velocity) is in 2d array va |
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| 236 | !----------------------------------------------------------------------- |
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[3259] | 237 | ! |
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| 238 | DO jk = 2, jpkm1 !== First recurrence : Dk = Dk - Lk * Uk-1 / Dk-1 (increasing k) == |
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| 239 | DO jj = 2, jpjm1 |
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| 240 | DO ji = fs_2, fs_jpim1 ! vector opt. |
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[3] | 241 | 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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| 242 | END DO |
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[3259] | 243 | END DO |
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| 244 | END DO |
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| 245 | ! |
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| 246 | DO jj = 2, jpjm1 !== second recurrence: SOLk = RHSk - Lk / Dk-1 Lk-1 == |
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| 247 | DO ji = fs_2, fs_jpim1 ! vector opt. |
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| 248 | 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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| 249 | & / ( fse3v(ji,jj,1) * rau0 ) ) |
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| 250 | END DO |
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| 251 | END DO |
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| 252 | DO jk = 2, jpkm1 |
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| 253 | DO jj = 2, jpjm1 |
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| 254 | DO ji = fs_2, fs_jpim1 ! vector opt. |
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[503] | 255 | zrhs = vb(ji,jj,jk) + p2dt * va(ji,jj,jk) ! zrhs=right hand side |
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[3] | 256 | va(ji,jj,jk) = zrhs - zwi(ji,jj,jk) / zwd(ji,jj,jk-1) * va(ji,jj,jk-1) |
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| 257 | END DO |
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[3259] | 258 | END DO |
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| 259 | END DO |
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| 260 | ! |
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| 261 | DO jj = 2, jpjm1 !== thrid recurrence : SOLk = ( Lk - Uk * SOLk+1 ) / Dk == |
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| 262 | DO ji = fs_2, fs_jpim1 ! vector opt. |
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| 263 | va(ji,jj,jpkm1) = va(ji,jj,jpkm1) / zwd(ji,jj,jpkm1) |
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| 264 | END DO |
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| 265 | END DO |
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| 266 | DO jk = jpk-2, 1, -1 |
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| 267 | DO jj = 2, jpjm1 |
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| 268 | DO ji = fs_2, fs_jpim1 ! vector opt. |
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| 269 | 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] | 270 | END DO |
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| 271 | END DO |
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| 272 | END DO |
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| 273 | |
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| 274 | ! Normalization to obtain the general momentum trend va |
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| 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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[2528] | 278 | va(ji,jj,jk) = ( va(ji,jj,jk) - vb(ji,jj,jk) ) * z1_p2dt |
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[3] | 279 | END DO |
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| 280 | END DO |
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| 281 | END DO |
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[3285] | 282 | |
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| 283 | !! restore bottom layer avmu(v) |
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| 284 | IF( ln_bfrimp ) THEN |
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| 285 | # if defined key_vectopt_loop |
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| 286 | DO jj = 1, 1 |
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| 287 | DO ji = jpi+2, jpij-jpi-1 ! vector opt. (forced unrolling) |
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| 288 | # else |
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| 289 | DO jj = 2, jpjm1 |
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| 290 | DO ji = 2, jpim1 |
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| 291 | # endif |
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| 292 | ikbu = mbku(ji,jj) ! ocean bottom level at u- and v-points |
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| 293 | ikbv = mbkv(ji,jj) ! (deepest ocean u- and v-points) |
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| 294 | avmu(ji,jj,ikbu+1) = zavmu(ji,jj) |
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| 295 | avmv(ji,jj,ikbv+1) = zavmv(ji,jj) |
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| 296 | END DO |
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| 297 | END DO |
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| 298 | ENDIF |
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[2528] | 299 | ! |
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[3285] | 300 | CALL wrk_dealloc( jpi,jpj,jpk, zwi, zwd, zws) |
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| 301 | CALL wrk_dealloc( jpi,jpj, zavmu, zavmv) |
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[2715] | 302 | ! |
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[3161] | 303 | IF( nn_timing == 1 ) CALL timing_stop('dyn_zdf_imp') |
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| 304 | ! |
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[3] | 305 | END SUBROUTINE dyn_zdf_imp |
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| 306 | |
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| 307 | !!============================================================================== |
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| 308 | END MODULE dynzdf_imp |
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