[456] | 1 | MODULE dynzdf_imp_jki |
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| 2 | !!============================================================================== |
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| 3 | !! *** MODULE dynzdf_imp_jki *** |
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| 4 | !! Ocean dynamics: vertical component(s) of the momentum mixing trend |
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| 5 | !!============================================================================== |
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[503] | 6 | !! History : 8.5 ! 02-08 (G. Madec) auto-tasking option |
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| 7 | !!---------------------------------------------------------------------- |
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[456] | 8 | |
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| 9 | !!---------------------------------------------------------------------- |
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| 10 | !! dyn_zdf_imp_jki : update the momentum trend with the vertical |
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| 11 | !! diffusion using an implicit time-stepping and |
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| 12 | !! j-k-i loops. |
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| 13 | !!---------------------------------------------------------------------- |
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| 14 | !! * Modules used |
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| 15 | USE oce ! ocean dynamics and tracers |
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| 16 | USE dom_oce ! ocean space and time domain |
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[708] | 17 | USE zdf_oce ! ocean vertical physics |
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| 18 | USE sbc_oce ! surface boundary condition: ocean |
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[456] | 19 | USE phycst ! physical constants |
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| 20 | USE in_out_manager ! I/O manager |
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| 21 | |
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| 22 | IMPLICIT NONE |
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| 23 | PRIVATE |
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| 24 | |
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| 25 | !! * Routine accessibility |
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| 26 | PUBLIC dyn_zdf_imp_jki ! called by step.F90 |
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| 27 | |
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| 28 | !! * Substitutions |
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| 29 | # include "domzgr_substitute.h90" |
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| 30 | # include "vectopt_loop_substitute.h90" |
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| 31 | !!---------------------------------------------------------------------- |
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| 32 | !! OPA 9.0 , LOCEAN-IPSL (2005) |
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[699] | 33 | !! $Id$ |
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[503] | 34 | !! Software governed by the CeCILL licence (modipsl/doc/NEMO_CeCILL.txt) |
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[456] | 35 | !!---------------------------------------------------------------------- |
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| 36 | |
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| 37 | CONTAINS |
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| 38 | |
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[503] | 39 | SUBROUTINE dyn_zdf_imp_jki( kt, p2dt ) |
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[456] | 40 | !!---------------------------------------------------------------------- |
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| 41 | !! *** ROUTINE dyn_zdf_imp_jki *** |
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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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| 50 | !! Surface boundary conditions: wind stress input |
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| 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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| 55 | !! ** Action : - Update (ua,va) arrays with the after vertical diffusive |
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| 56 | !! mixing trend. |
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| 57 | !!--------------------------------------------------------------------- |
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| 58 | !! * Arguments |
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[503] | 59 | INTEGER , INTENT( in ) :: kt ! ocean time-step index |
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| 60 | REAL(wp), INTENT( in ) :: p2dt ! ocean time-step index |
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[456] | 61 | |
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| 62 | !! * Local declarations |
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[503] | 63 | INTEGER :: ji, jj, jk ! dummy loop indices |
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| 64 | INTEGER :: ikst, ikenm2, ikstp1 ! temporary integers |
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| 65 | REAL(wp) :: zrau0r, z2dtf, zcoef, zzws ! temporary scalars |
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| 66 | REAL(wp), DIMENSION(jpi,jpk) :: zwx, zwy, zwz, & ! workspace |
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| 67 | & zwd, zws, zwi, zwt |
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[456] | 68 | !!---------------------------------------------------------------------- |
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| 69 | |
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| 70 | IF( kt == nit000 ) THEN |
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| 71 | IF(lwp) WRITE(numout,*) |
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| 72 | IF(lwp) WRITE(numout,*) 'dyn_zdf_imp_jki : vertical momentum diffusion implicit operator' |
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| 73 | IF(lwp) WRITE(numout,*) '~~~~~~~~~~~~~~~ auto-task case (j-k-i loop)' |
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| 74 | ENDIF |
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| 75 | |
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| 76 | |
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| 77 | ! 0. Local constant initialization |
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| 78 | ! -------------------------------- |
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| 79 | zrau0r = 1. / rau0 ! inverse of the reference density |
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| 80 | |
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| 81 | ! ! =============== |
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| 82 | DO jj = 2, jpjm1 ! Vertical slab |
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| 83 | ! ! =============== |
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| 84 | ! 1. Vertical diffusion on u |
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| 85 | ! --------------------------- |
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| 86 | |
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| 87 | ! Matrix and second member construction |
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| 88 | ! bottom boundary condition: only zws must be masked as avmu can take |
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| 89 | ! non zero value at the ocean bottom depending on the bottom friction |
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| 90 | ! used (see zdfmix.F) |
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| 91 | DO jk = 1, jpkm1 |
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| 92 | DO ji = 2, jpim1 |
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[503] | 93 | zcoef = - p2dt / fse3u(ji,jj,jk) |
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[456] | 94 | zwi(ji,jk) = zcoef * avmu(ji,jj,jk ) / fse3uw(ji,jj,jk ) |
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| 95 | zzws = zcoef * avmu(ji,jj,jk+1) / fse3uw(ji,jj,jk+1) |
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| 96 | zws(ji,jk) = zzws * umask(ji,jj,jk+1) |
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| 97 | zwd(ji,jk) = 1. - zwi(ji,jk) - zzws |
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[503] | 98 | zwy(ji,jk) = ub(ji,jj,jk) + p2dt * ua(ji,jj,jk) |
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[456] | 99 | END DO |
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| 100 | END DO |
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| 101 | |
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| 102 | ! Surface boudary conditions |
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| 103 | DO ji = 2, jpim1 |
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[503] | 104 | z2dtf = p2dt / ( fse3u(ji,jj,1)*rau0 ) |
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[456] | 105 | zwi(ji,1) = 0. |
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| 106 | zwd(ji,1) = 1. - zws(ji,1) |
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[710] | 107 | zwy(ji,1) = zwy(ji,1) + z2dtf * utau(ji,jj) |
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[456] | 108 | END DO |
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| 109 | |
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| 110 | ! Matrix inversion starting from the first level |
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| 111 | ikst = 1 |
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| 112 | !!---------------------------------------------------------------------- |
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| 113 | !! ZDF.MATRIXSOLVER |
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| 114 | !! ******************** |
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| 115 | !!---------------------------------------------------------------------- |
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| 116 | !! Matrix inversion |
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| 117 | ! solve m.x = y where m is a tri diagonal matrix ( jpk*jpk ) |
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| 118 | ! |
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| 119 | ! ( zwd1 zws1 0 0 0 )( zwx1 ) ( zwy1 ) |
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| 120 | ! ( zwi2 zwd2 zws2 0 0 )( zwx2 ) ( zwy2 ) |
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| 121 | ! ( 0 zwi3 zwd3 zws3 0 )( zwx3 )=( zwy3 ) |
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| 122 | ! ( ... )( ... ) ( ... ) |
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| 123 | ! ( 0 0 0 zwik zwdk )( zwxk ) ( zwyk ) |
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| 124 | ! |
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| 125 | ! m is decomposed in the product of an upper and lower triangular |
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| 126 | ! matrix |
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| 127 | ! The 3 diagonal terms are in 2d arrays: zwd, zws, zwi |
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| 128 | ! The second member is in 2d array zwy |
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| 129 | ! The solution is in 2d array zwx |
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| 130 | ! The 2d arry zwt and zwz are work space arrays |
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| 131 | ! |
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| 132 | ! N.B. the starting vertical index (ikst) is equal to 1 except for |
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| 133 | ! the resolution of tke matrix where surface tke value is prescribed |
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| 134 | ! so that ikstrt=2. |
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| 135 | !!---------------------------------------------------------------------- |
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| 136 | |
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| 137 | ikstp1 = ikst + 1 |
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| 138 | ikenm2 = jpk - 2 |
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| 139 | DO ji = 2, jpim1 |
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| 140 | zwt(ji,ikst) = zwd(ji,ikst) |
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| 141 | END DO |
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| 142 | DO jk = ikstp1, jpkm1 |
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| 143 | DO ji = 2, jpim1 |
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| 144 | zwt(ji,jk) = zwd(ji,jk) - zwi(ji,jk) * zws(ji,jk-1) / zwt(ji,jk-1) |
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| 145 | END DO |
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| 146 | END DO |
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| 147 | DO ji = 2, jpim1 |
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| 148 | zwz(ji,ikst) = zwy(ji,ikst) |
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| 149 | END DO |
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| 150 | DO jk = ikstp1, jpkm1 |
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| 151 | DO ji = 2, jpim1 |
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| 152 | zwz(ji,jk) = zwy(ji,jk) - zwi(ji,jk) / zwt(ji,jk-1) * zwz(ji,jk-1) |
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| 153 | END DO |
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| 154 | END DO |
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| 155 | DO ji = 2, jpim1 |
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| 156 | zwx(ji,jpkm1) = zwz(ji,jpkm1) / zwt(ji,jpkm1) |
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| 157 | END DO |
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| 158 | DO jk = ikenm2, ikst, -1 |
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| 159 | DO ji = 2, jpim1 |
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| 160 | zwx(ji,jk) =( zwz(ji,jk) - zws(ji,jk) * zwx(ji,jk+1) ) / zwt(ji,jk) |
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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 ji = 2, jpim1 |
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[503] | 167 | ua(ji,jj,jk) = ( zwx(ji,jk) - ub(ji,jj,jk) ) / p2dt |
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[456] | 168 | END DO |
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| 169 | END DO |
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| 170 | |
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| 171 | |
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| 172 | ! 2. Vertical diffusion on v |
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| 173 | ! --------------------------- |
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| 174 | ! Matrix and second member construction |
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| 175 | ! bottom boundary condition: only zws must be masked as avmv can take |
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| 176 | ! non zero value at the ocean bottom depending on the bottom friction |
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| 177 | ! used (see zdfmix.F) |
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| 178 | DO jk = 1, jpkm1 |
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| 179 | DO ji = 2, jpim1 |
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[503] | 180 | zcoef = -p2dt/fse3v(ji,jj,jk) |
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[456] | 181 | zwi(ji,jk) = zcoef * avmv(ji,jj,jk ) / fse3vw(ji,jj,jk ) |
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| 182 | zzws = zcoef * avmv(ji,jj,jk+1) / fse3vw(ji,jj,jk+1) |
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| 183 | zws(ji,jk) = zzws * vmask(ji,jj,jk+1) |
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| 184 | zwd(ji,jk) = 1. - zwi(ji,jk) - zzws |
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[503] | 185 | zwy(ji,jk) = vb(ji,jj,jk) + p2dt * va(ji,jj,jk) |
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[456] | 186 | END DO |
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| 187 | END DO |
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| 188 | |
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| 189 | ! Surface boudary conditions |
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| 190 | DO ji = 2, jpim1 |
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[503] | 191 | z2dtf = p2dt / ( fse3v(ji,jj,1)*rau0 ) |
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[456] | 192 | zwi(ji,1) = 0.e0 |
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| 193 | zwd(ji,1) = 1. - zws(ji,1) |
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[710] | 194 | zwy(ji,1) = zwy(ji,1) + z2dtf * vtau(ji,jj) |
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[456] | 195 | END DO |
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| 196 | |
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| 197 | ! Matrix inversion starting from the first level |
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| 198 | ikst = 1 |
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| 199 | !!---------------------------------------------------------------------- |
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| 200 | !! ZDF.MATRIXSOLVER |
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| 201 | !! ******************** |
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| 202 | !!---------------------------------------------------------------------- |
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| 203 | !! Matrix inversion |
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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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| 212 | ! m is decomposed in the product of an upper and lower triangular |
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| 213 | ! matrix |
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| 214 | ! The 3 diagonal terms are in 2d arrays: zwd, zws, zwi |
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| 215 | ! The second member is in 2d array zwy |
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| 216 | ! The solution is in 2d array zwx |
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| 217 | ! The 2d arry zwt and zwz are work space arrays |
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| 218 | ! |
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| 219 | ! N.B. the starting vertical index (ikst) is equal to 1 except for |
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| 220 | ! the resolution of tke matrix where surface tke value is prescribed |
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| 221 | ! so that ikstrt=2. |
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| 222 | !!---------------------------------------------------------------------- |
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| 223 | |
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| 224 | ikstp1 = ikst + 1 |
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| 225 | ikenm2 = jpk - 2 |
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| 226 | DO ji = 2, jpim1 |
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| 227 | zwt(ji,ikst) = zwd(ji,ikst) |
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| 228 | END DO |
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| 229 | DO jk = ikstp1, jpkm1 |
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| 230 | DO ji = 2, jpim1 |
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| 231 | zwt(ji,jk) = zwd(ji,jk) - zwi(ji,jk) * zws(ji,jk-1) / zwt(ji,jk-1) |
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| 232 | END DO |
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| 233 | END DO |
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| 234 | DO ji = 2, jpim1 |
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| 235 | zwz(ji,ikst) = zwy(ji,ikst) |
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| 236 | END DO |
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| 237 | DO jk = ikstp1, jpkm1 |
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| 238 | DO ji = 2, jpim1 |
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| 239 | zwz(ji,jk) = zwy(ji,jk) - zwi(ji,jk) / zwt(ji,jk-1) * zwz(ji,jk-1) |
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| 240 | END DO |
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| 241 | END DO |
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| 242 | DO ji = 2, jpim1 |
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| 243 | zwx(ji,jpkm1) = zwz(ji,jpkm1) / zwt(ji,jpkm1) |
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| 244 | END DO |
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| 245 | DO jk = ikenm2, ikst, -1 |
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| 246 | DO ji = 2, jpim1 |
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| 247 | zwx(ji,jk) =( zwz(ji,jk) - zws(ji,jk) * zwx(ji,jk+1) ) / zwt(ji,jk) |
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| 248 | END DO |
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| 249 | END DO |
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| 250 | |
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| 251 | ! Normalization to obtain the general momentum trend va |
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| 252 | DO jk = 1, jpkm1 |
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| 253 | DO ji = 2, jpim1 |
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[503] | 254 | va(ji,jj,jk) = ( zwx(ji,jk) - vb(ji,jj,jk) ) / p2dt |
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[456] | 255 | END DO |
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| 256 | END DO |
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| 257 | ! ! =============== |
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| 258 | END DO ! End of slab |
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| 259 | ! ! =============== |
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| 260 | |
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| 261 | END SUBROUTINE dyn_zdf_imp_jki |
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| 262 | |
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| 263 | !!============================================================================== |
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| 264 | END MODULE dynzdf_imp_jki |
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