| 1 | MODULE dynzdf_imp_tam |
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| 2 | #ifdef key_tam |
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| 3 | !!============================================================================== |
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| 4 | !! *** MODULE dynzdf_imp_tam *** |
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| 5 | !! Ocean dynamics: vertical component(s) of the momentum mixing trend |
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| 6 | !! Tangent and Adjoint Module |
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| 7 | !!============================================================================== |
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| 8 | !! History of the direct module: |
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| 9 | !! ! 90-10 (B. Blanke) Original code |
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| 10 | !! ! 97-05 (G. Madec) vertical component of isopycnal |
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| 11 | !! 8.5 ! 02-08 (G. Madec) F90: Free form and module |
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| 12 | !! History of the TAM module: |
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| 13 | !! 9.0 ! 09-01 (A. Vidard) TAM of the 02-08 version |
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| 14 | !!---------------------------------------------------------------------- |
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| 15 | |
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| 16 | !!---------------------------------------------------------------------- |
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| 17 | !! dyn_zdf_imp : update the momentum trend with the vertical diffu- |
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| 18 | !! sion using an implicit time-stepping scheme. |
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| 19 | !!---------------------------------------------------------------------- |
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| 20 | !! * Modules used |
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| 21 | USE par_kind , ONLY: & ! Precision variables |
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| 22 | & wp |
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| 23 | USE par_oce , ONLY: & ! Ocean space and time domain variables |
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| 24 | & jpi, & |
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| 25 | & jpj, & |
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| 26 | & jpk, & |
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| 27 | & jpim1, & |
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| 28 | & jpjm1, & |
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| 29 | & jpkm1 |
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| 30 | USE oce_tam , ONLY: & ! ocean dynamics and tracers |
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| 31 | & ub_tl, & |
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| 32 | & ua_tl, & |
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| 33 | & vb_tl, & |
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| 34 | & va_tl, & |
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| 35 | & ub_ad, & |
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| 36 | & ua_ad, & |
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| 37 | & vb_ad, & |
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| 38 | & va_ad |
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| 39 | USE zdf_oce , ONLY: & ! ocean vertical physics |
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| 40 | & avmu, & |
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| 41 | & avmv |
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| 42 | USE dom_oce , ONLY: & ! ocean space and time domain |
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| 43 | #if defined key_zco |
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| 44 | & e3t_0, & |
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| 45 | & e3w_0, & |
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| 46 | #else |
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| 47 | & e3u, & |
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| 48 | & e3v, & |
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| 49 | & e3uw, & |
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| 50 | & e3vw, & |
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| 51 | #endif |
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| 52 | & umask, & |
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| 53 | & vmask |
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| 54 | USE phycst , ONLY: & ! physical constants |
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| 55 | & rau0 |
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| 56 | USE in_out_manager, ONLY: & ! I/O manager |
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| 57 | & nit000, & |
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| 58 | & nitend, & |
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| 59 | & numout, & |
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| 60 | & lwp |
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| 61 | |
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| 62 | |
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| 63 | IMPLICIT NONE |
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| 64 | PRIVATE |
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| 65 | |
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| 66 | !! * Routine accessibility |
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| 67 | PUBLIC dyn_zdf_imp_tan ! called by dynzdf_tam.F90 |
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| 68 | PUBLIC dyn_zdf_imp_adj ! called by dynzdf_tam.F90 |
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| 69 | |
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| 70 | !! * Substitutions |
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| 71 | # include "domzgr_substitute.h90" |
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| 72 | # include "vectopt_loop_substitute.h90" |
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| 73 | !!---------------------------------------------------------------------- |
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| 74 | |
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| 75 | CONTAINS |
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| 76 | |
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| 77 | SUBROUTINE dyn_zdf_imp_tan( kt, p2dt ) |
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| 78 | !!---------------------------------------------------------------------- |
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| 79 | !! *** ROUTINE dyn_zdf_imp_tan *** |
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| 80 | !! |
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| 81 | !! ** Purpose of the direct routine: |
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| 82 | !! Compute the trend due to the vert. momentum diffusion |
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| 83 | !! and the surface forcing, and add it to the general trend of |
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| 84 | !! the momentum equations. |
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| 85 | !! |
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| 86 | !! ** Method of the direct routine: |
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| 87 | !! The vertical momentum mixing trend is given by : |
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| 88 | !! dz( avmu dz(u) ) = 1/e3u dk+1( avmu/e3uw dk(ua) ) |
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| 89 | !! backward time stepping |
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| 90 | !! Surface boundary conditions: wind stress input |
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| 91 | !! Bottom boundary conditions : bottom stress (cf zdfbfr.F) |
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| 92 | !! Add this trend to the general trend ua : |
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| 93 | !! ua = ua + dz( avmu dz(u) )E |
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| 94 | !! |
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| 95 | !! ** Action : - Update (ua,va) arrays with the after vertical diffusive |
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| 96 | !! mixing trend. |
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| 97 | !!--------------------------------------------------------------------- |
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| 98 | !! * Modules used |
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| 99 | !! * Arguments |
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| 100 | INTEGER , INTENT( in ) :: kt ! ocean time-step index |
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| 101 | REAL(wp), INTENT( in ) :: p2dt ! time-step |
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| 102 | |
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| 103 | !! * Local declarations |
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| 104 | INTEGER :: ji, jj, jk ! dummy loop indices |
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| 105 | REAL(wp) :: zrau0r, z2dtf, zcoef, zzws, zrhstl ! temporary scalars |
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| 106 | REAL(wp), DIMENSION(jpi,jpj,jpk):: zwi, zws, zwd ! temporary workspace arrays |
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| 107 | !!---------------------------------------------------------------------- |
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| 108 | |
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| 109 | IF( kt == nit000 ) THEN |
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| 110 | IF(lwp) WRITE(numout,*) |
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| 111 | IF(lwp) WRITE(numout,*) 'dyn_zdf_imp_tan : vertical momentum diffusion explicit operator' |
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| 112 | IF(lwp) WRITE(numout,*) '~~~~~~~~~~~~~~~ ' |
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| 113 | ENDIF |
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| 114 | ! 0. Local constant initialization |
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| 115 | ! -------------------------------- |
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| 116 | zrau0r = 1. / rau0 ! inverse of the reference density |
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| 117 | |
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| 118 | ! 1. Vertical diffusion on u |
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| 119 | ! --------------------------- |
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| 120 | ! Matrix and second member construction |
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| 121 | ! non zero value at the ocean bottom depending on the bottom friction |
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| 122 | ! used but the bottom velocities have already been updated with the bottom |
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| 123 | ! friction velocity in dyn_bfr using values from the previous timestep. There |
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| 124 | ! is no need to include these in the implicit calculation. |
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| 125 | DO jk = 1, jpkm1 |
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| 126 | DO jj = 2, jpjm1 |
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| 127 | DO ji = fs_2, fs_jpim1 ! vector opt. |
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| 128 | zcoef = - p2dt / fse3u(ji,jj,jk) |
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| 129 | zwi(ji,jj,jk) = zcoef * avmu(ji,jj,jk ) / fse3uw(ji,jj,jk ) * umask(ji,jj,jk) |
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| 130 | zzws = zcoef * avmu(ji,jj,jk+1) / fse3uw(ji,jj,jk+1) |
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| 131 | zws(ji,jj,jk) = zzws * umask(ji,jj,jk+1) |
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| 132 | zwd(ji,jj,jk) = 1. - zwi(ji,jj,jk) - zzws |
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| 133 | END DO |
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| 134 | END DO |
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| 135 | END DO |
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| 136 | |
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| 137 | ! Surface boudary conditions |
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| 138 | DO jj = 2, jpjm1 |
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| 139 | DO ji = fs_2, fs_jpim1 ! vector opt. |
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| 140 | zwi(ji,jj,1) = 0.0_wp |
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| 141 | zwd(ji,jj,1) = 1. - zws(ji,jj,1) |
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| 142 | END DO |
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| 143 | END DO |
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| 144 | |
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| 145 | ! Matrix inversion starting from the first level |
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| 146 | !----------------------------------------------------------------------- |
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| 147 | ! solve m.x = y where m is a tri diagonal matrix ( jpk*jpk ) |
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| 148 | ! |
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| 149 | ! ( zwd1 zws1 0 0 0 )( zwx1 ) ( zwy1 ) |
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| 150 | ! ( zwi2 zwd2 zws2 0 0 )( zwx2 ) ( zwy2 ) |
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| 151 | ! ( 0 zwi3 zwd3 zws3 0 )( zwx3 )=( zwy3 ) |
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| 152 | ! ( ... )( ... ) ( ... ) |
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| 153 | ! ( 0 0 0 zwik zwdk )( zwxk ) ( zwyk ) |
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| 154 | ! |
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| 155 | ! m is decomposed in the product of an upper and a lower triangular matrix |
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| 156 | ! The 3 diagonal terms are in 2d arrays: zwd, zws, zwi |
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| 157 | ! The solution (the after velocity) is in ua |
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| 158 | !----------------------------------------------------------------------- |
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| 159 | |
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| 160 | ! First recurrence : Dk = Dk - Lk * Uk-1 / Dk-1 (increasing k) |
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| 161 | DO jk = 2, jpkm1 |
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| 162 | DO jj = 2, jpjm1 |
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| 163 | DO ji = fs_2, fs_jpim1 ! vector opt. |
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| 164 | 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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| 165 | END DO |
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| 166 | END DO |
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| 167 | END DO |
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| 168 | |
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| 169 | ! second recurrence: SOLk = RHSk - Lk / Dk-1 Lk-1 |
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| 170 | DO jj = 2, jpjm1 |
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| 171 | DO ji = fs_2, fs_jpim1 ! vector opt. |
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| 172 | ua_tl(ji,jj,1) = ub_tl(ji,jj,1) & |
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| 173 | + p2dt * ua_tl(ji,jj,1) |
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| 174 | END DO |
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| 175 | END DO |
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| 176 | DO jk = 2, jpkm1 |
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| 177 | DO jj = 2, jpjm1 |
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| 178 | DO ji = fs_2, fs_jpim1 ! vector opt. |
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| 179 | zrhstl = ub_tl(ji,jj,jk) + p2dt * ua_tl(ji,jj,jk) ! zrhs=right hand side |
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| 180 | ua_tl(ji,jj,jk) = zrhstl - zwi(ji,jj,jk) / zwd(ji,jj,jk-1) * ua_tl(ji,jj,jk-1) |
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| 181 | END DO |
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| 182 | END DO |
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| 183 | END DO |
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| 184 | |
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| 185 | ! thrid recurrence : SOLk = ( Lk - Uk * Ek+1 ) / Dk |
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| 186 | DO jj = 2, jpjm1 |
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| 187 | DO ji = fs_2, fs_jpim1 ! vector opt. |
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| 188 | ua_tl(ji,jj,jpkm1) = ua_tl(ji,jj,jpkm1) / zwd(ji,jj,jpkm1) |
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| 189 | END DO |
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| 190 | END DO |
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| 191 | DO jk = jpk-2, 1, -1 |
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| 192 | DO jj = 2, jpjm1 |
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| 193 | DO ji = fs_2, fs_jpim1 ! vector opt. |
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| 194 | ua_tl(ji,jj,jk) = ( ua_tl(ji,jj,jk) - zws(ji,jj,jk) * ua_tl(ji,jj,jk+1) ) / zwd(ji,jj,jk) |
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| 195 | END DO |
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| 196 | END DO |
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| 197 | END DO |
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| 198 | |
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| 199 | ! Normalization to obtain the general momentum trend ua |
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| 200 | DO jk = 1, jpkm1 |
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| 201 | DO jj = 2, jpjm1 |
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| 202 | DO ji = fs_2, fs_jpim1 ! vector opt. |
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| 203 | ua_tl(ji,jj,jk) = ( ua_tl(ji,jj,jk) - ub_tl(ji,jj,jk) ) / p2dt |
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| 204 | END DO |
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| 205 | END DO |
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| 206 | END DO |
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| 207 | |
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| 208 | |
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| 209 | ! 2. Vertical diffusion on v |
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| 210 | ! --------------------------- |
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| 211 | ! Matrix and second member construction |
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| 212 | ! bottom boundary condition: both zwi and zws must be masked as avmv can take |
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| 213 | ! non zero value at the ocean bottom depending on the bottom friction |
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| 214 | ! used but the bottom velocities have already been updated with the bottom |
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| 215 | ! friction velocity in dyn_bfr using values from the previous timestep. There |
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| 216 | ! is no need to include these in the implicit calculation. |
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| 217 | DO jk = 1, jpkm1 |
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| 218 | DO jj = 2, jpjm1 |
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| 219 | DO ji = fs_2, fs_jpim1 ! vector opt. |
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| 220 | zcoef = -p2dt / fse3v(ji,jj,jk) |
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| 221 | zwi(ji,jj,jk) = zcoef * avmv(ji,jj,jk ) / fse3vw(ji,jj,jk ) * vmask(ji,jj,jk) |
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| 222 | zzws = zcoef * avmv(ji,jj,jk+1) / fse3vw(ji,jj,jk+1) |
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| 223 | zws(ji,jj,jk) = zzws * vmask(ji,jj,jk+1) |
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| 224 | zwd(ji,jj,jk) = 1. - zwi(ji,jj,jk) - zzws |
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| 225 | END DO |
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| 226 | END DO |
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| 227 | END DO |
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| 228 | |
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| 229 | ! Surface boudary conditions |
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| 230 | DO jj = 2, jpjm1 |
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| 231 | DO ji = fs_2, fs_jpim1 ! vector opt. |
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| 232 | zwi(ji,jj,1) = 0._wp |
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| 233 | zwd(ji,jj,1) = 1. - zws(ji,jj,1) |
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| 234 | END DO |
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| 235 | END DO |
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| 236 | |
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| 237 | ! Matrix inversion |
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| 238 | !----------------------------------------------------------------------- |
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| 239 | ! solve m.x = y where m is a tri diagonal matrix ( jpk*jpk ) |
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| 240 | ! |
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| 241 | ! ( zwd1 zws1 0 0 0 )( zwx1 ) ( zwy1 ) |
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| 242 | ! ( zwi2 zwd2 zws2 0 0 )( zwx2 ) ( zwy2 ) |
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| 243 | ! ( 0 zwi3 zwd3 zws3 0 )( zwx3 )=( zwy3 ) |
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| 244 | ! ( ... )( ... ) ( ... ) |
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| 245 | ! ( 0 0 0 zwik zwdk )( zwxk ) ( zwyk ) |
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| 246 | ! |
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| 247 | ! m is decomposed in the product of an upper and lower triangular |
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| 248 | ! matrix |
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| 249 | ! The 3 diagonal terms are in 2d arrays: zwd, zws, zwi |
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| 250 | ! The solution (after velocity) is in 2d array va |
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| 251 | !----------------------------------------------------------------------- |
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| 252 | |
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| 253 | ! First recurrence : Dk = Dk - Lk * Uk-1 / Dk-1 (increasing k) |
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| 254 | DO jk = 2, 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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| 257 | 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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| 258 | END DO |
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| 259 | END DO |
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| 260 | END DO |
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| 261 | |
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| 262 | ! second recurrence: SOLk = RHSk - Lk / Dk-1 Lk-1 |
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| 263 | DO jj = 2, jpjm1 |
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| 264 | DO ji = fs_2, fs_jpim1 ! vector opt. |
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| 265 | va_tl(ji,jj,1) = vb_tl(ji,jj,1) & |
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| 266 | + p2dt * va_tl(ji,jj,1) |
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| 267 | END DO |
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| 268 | END DO |
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| 269 | DO jk = 2, jpkm1 |
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| 270 | DO jj = 2, jpjm1 |
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| 271 | DO ji = fs_2, fs_jpim1 ! vector opt. |
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| 272 | zrhstl = vb_tl(ji,jj,jk) + p2dt * va_tl(ji,jj,jk) ! zrhs=right hand side |
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| 273 | va_tl(ji,jj,jk) = zrhstl - zwi(ji,jj,jk) / zwd(ji,jj,jk-1) * va_tl(ji,jj,jk-1) |
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| 274 | END DO |
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| 275 | END DO |
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| 276 | END DO |
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| 277 | |
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| 278 | ! thrid recurrence : SOLk = ( Lk - Uk * SOLk+1 ) / Dk |
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| 279 | DO jj = 2, jpjm1 |
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| 280 | DO ji = fs_2, fs_jpim1 ! vector opt. |
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| 281 | va_tl(ji,jj,jpkm1) = va_tl(ji,jj,jpkm1) / zwd(ji,jj,jpkm1) |
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| 282 | END DO |
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| 283 | END DO |
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| 284 | DO jk = jpk-2, 1, -1 |
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| 285 | DO jj = 2, jpjm1 |
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| 286 | DO ji = fs_2, fs_jpim1 ! vector opt. |
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| 287 | va_tl(ji,jj,jk) = ( va_tl(ji,jj,jk) - zws(ji,jj,jk) * va_tl(ji,jj,jk+1) ) / zwd(ji,jj,jk) |
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| 288 | END DO |
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| 289 | END DO |
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| 290 | END DO |
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| 291 | |
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| 292 | ! Normalization to obtain the general momentum trend va |
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| 293 | DO jk = 1, jpkm1 |
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| 294 | DO jj = 2, jpjm1 |
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| 295 | DO ji = fs_2, fs_jpim1 ! vector opt. |
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| 296 | va_tl(ji,jj,jk) = ( va_tl(ji,jj,jk) - vb_tl(ji,jj,jk) ) / p2dt |
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| 297 | END DO |
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| 298 | END DO |
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| 299 | END DO |
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| 300 | |
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| 301 | END SUBROUTINE dyn_zdf_imp_tan |
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| 302 | SUBROUTINE dyn_zdf_imp_adj( kt, p2dt ) |
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| 303 | !!---------------------------------------------------------------------- |
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| 304 | !! *** ROUTINE dyn_zdf_imp_adj *** |
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| 305 | !! |
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| 306 | !! ** Purpose of the direct routine: |
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| 307 | !! Compute the trend due to the vert. momentum diffusion |
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| 308 | !! and the surface forcing, and add it to the general trend of |
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| 309 | !! the momentum equations. |
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| 310 | !! |
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| 311 | !! ** Method of the direct routine: |
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| 312 | !! The vertical momentum mixing trend is given by : |
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| 313 | !! dz( avmu dz(u) ) = 1/e3u dk+1( avmu/e3uw dk(ua) ) |
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| 314 | !! backward time stepping |
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| 315 | !! Surface boundary conditions: wind stress input |
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| 316 | !! Bottom boundary conditions : bottom stress (cf zdfbfr.F) |
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| 317 | !! Add this trend to the general trend ua : |
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| 318 | !! ua = ua + dz( avmu dz(u) )E |
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| 319 | !! |
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| 320 | !! ** Action : - Update (ua,va) arrays with the after vertical diffusive |
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| 321 | !! mixing trend. |
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| 322 | !!--------------------------------------------------------------------- |
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| 323 | !! * Modules used |
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| 324 | !! * Arguments |
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| 325 | INTEGER , INTENT( in ) :: kt ! ocean time-step index |
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| 326 | REAL(wp), INTENT( in ) :: p2dt ! time-step |
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| 327 | |
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| 328 | !! * Local declarations |
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| 329 | !! * Local declarations |
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| 330 | INTEGER :: ji, jj, jk ! dummy loop indices |
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| 331 | REAL(wp) :: zrau0r, z2dtf, zcoef, zzws, zrhsad ! temporary scalars |
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| 332 | REAL(wp), DIMENSION(jpi,jpj,jpk) :: zwi, zws, zwd! temporary workspace arrays |
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| 333 | !!---------------------------------------------------------------------- |
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| 334 | |
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| 335 | IF( kt == nitend ) THEN |
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| 336 | IF(lwp) WRITE(numout,*) |
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| 337 | IF(lwp) WRITE(numout,*) 'dyn_zdf_imp_adj : vertical momentum diffusion explicit operator' |
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| 338 | IF(lwp) WRITE(numout,*) '~~~~~~~~~~~~~~~ ' |
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| 339 | ENDIF |
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| 340 | ! 0. Local constant initialization |
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| 341 | ! -------------------------------- |
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| 342 | zrau0r = 1. / rau0 ! inverse of the reference density |
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| 343 | zrhsad = 0.0_wp |
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| 344 | |
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| 345 | ! 2. Vertical diffusion on v |
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| 346 | ! --------------------------- |
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| 347 | ! Matrix and second member construction |
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| 348 | ! bottom boundary condition: both zwi and zws must be masked as avmv can take |
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| 349 | ! non zero value at the ocean bottom depending on the bottom friction |
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| 350 | ! used but the bottom velocities have already been updated with the bottom |
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| 351 | ! friction velocity in dyn_bfr using values from the previous timestep. There |
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| 352 | ! is no need to include these in the implicit calculation. |
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| 353 | DO jk = 1, jpkm1 |
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| 354 | DO jj = 2, jpjm1 |
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| 355 | DO ji = fs_2, fs_jpim1 ! vector opt. |
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| 356 | zcoef = -p2dt / fse3v(ji,jj,jk) |
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| 357 | zwi(ji,jj,jk) = zcoef * avmv(ji,jj,jk ) / fse3vw(ji,jj,jk ) * vmask(ji,jj,jk) |
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| 358 | zzws = zcoef * avmv(ji,jj,jk+1) / fse3vw(ji,jj,jk+1) |
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| 359 | zws(ji,jj,jk) = zzws * vmask(ji,jj,jk+1) |
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| 360 | zwd(ji,jj,jk) = 1._wp - zwi(ji,jj,jk) - zzws |
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| 361 | END DO |
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| 362 | END DO |
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| 363 | END DO |
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| 364 | |
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| 365 | ! Surface boudary conditions |
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| 366 | DO jj = 2, jpjm1 |
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| 367 | DO ji = fs_2, fs_jpim1 ! vector opt. |
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| 368 | zwi(ji,jj,1) = 0._wp |
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| 369 | zwd(ji,jj,1) = 1._wp - zws(ji,jj,1) |
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| 370 | END DO |
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| 371 | END DO |
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| 372 | |
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| 373 | ! Matrix inversion |
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| 374 | !----------------------------------------------------------------------- |
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| 375 | ! solve m.x = y where m is a tri diagonal matrix ( jpk*jpk ) |
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| 376 | ! |
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| 377 | ! ( zwd1 zws1 0 0 0 )( zwx1 ) ( zwy1 ) |
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| 378 | ! ( zwi2 zwd2 zws2 0 0 )( zwx2 ) ( zwy2 ) |
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| 379 | ! ( 0 zwi3 zwd3 zws3 0 )( zwx3 )=( zwy3 ) |
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| 380 | ! ( ... )( ... ) ( ... ) |
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| 381 | ! ( 0 0 0 zwik zwdk )( zwxk ) ( zwyk ) |
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| 382 | ! |
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| 383 | ! m is decomposed in the product of an upper and lower triangular |
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| 384 | ! matrix |
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| 385 | ! The 3 diagonal terms are in 2d arrays: zwd, zws, zwi |
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| 386 | ! The solution (after velocity) is in 2d array va |
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| 387 | !----------------------------------------------------------------------- |
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| 388 | |
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| 389 | ! First recurrence : Dk = Dk - Lk * Uk-1 / Dk-1 (increasing k) |
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| 390 | DO jk = 2, jpkm1 |
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| 391 | DO jj = 2, jpjm1 |
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| 392 | DO ji = fs_2, fs_jpim1 ! vector opt. |
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| 393 | 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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| 394 | END DO |
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| 395 | END DO |
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| 396 | END DO |
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| 397 | |
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| 398 | ! Normalization to obtain the general momentum trend va |
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| 399 | DO jk = jpkm1, 1, -1 |
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| 400 | DO jj = jpjm1, 2, -1 |
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| 401 | DO ji = fs_jpim1, fs_2, -1 ! vector opt. |
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| 402 | vb_ad(ji,jj,jk) = vb_ad(ji,jj,jk) - va_ad(ji,jj,jk) / p2dt |
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| 403 | va_ad(ji,jj,jk) = va_ad(ji,jj,jk) / p2dt |
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| 404 | END DO |
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| 405 | END DO |
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| 406 | END DO |
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| 407 | ! thrid recurrence : SOLk = ( Lk - Uk * SOLk+1 ) / Dk |
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| 408 | DO jk = 1, jpk-2 |
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| 409 | DO jj = jpjm1, 2, -1 |
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| 410 | DO ji = fs_jpim1, fs_2, -1 ! vector opt. |
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| 411 | va_ad(ji,jj,jk+1) = va_ad(ji,jj,jk+1) - zws(ji,jj,jk) * va_ad(ji,jj,jk) / zwd(ji,jj,jk) |
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| 412 | va_ad(ji,jj,jk ) = va_ad(ji,jj,jk ) / zwd(ji,jj,jk) |
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| 413 | END DO |
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| 414 | END DO |
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| 415 | END DO |
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| 416 | DO jj = jpjm1, 2, -1 |
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| 417 | DO ji = fs_jpim1, fs_2, -1 ! vector opt. |
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| 418 | va_ad(ji,jj,jpkm1) = va_ad(ji,jj,jpkm1) / zwd(ji,jj,jpkm1) |
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| 419 | END DO |
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| 420 | END DO |
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| 421 | ! second recurrence: SOLk = RHSk - Lk / Dk-1 Lk-1 |
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| 422 | DO jk = jpkm1, 2, -1 |
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| 423 | DO jj = jpjm1, 2, -1 |
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| 424 | DO ji = fs_jpim1, fs_2, -1 ! vector opt. |
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| 425 | zrhsad = zrhsad + va_ad(ji,jj,jk) |
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| 426 | va_ad(ji,jj,jk-1) = va_ad(ji,jj,jk-1) - zwi(ji,jj,jk) / zwd(ji,jj,jk-1) * va_ad(ji,jj,jk) |
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| 427 | va_ad(ji,jj,jk ) = 0.0_wp |
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| 428 | vb_ad(ji,jj,jk) = vb_ad(ji,jj,jk) + zrhsad |
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| 429 | va_ad(ji,jj,jk) = va_ad(ji,jj,jk) + p2dt * zrhsad |
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| 430 | zrhsad = 0.0_wp |
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| 431 | END DO |
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| 432 | END DO |
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| 433 | END DO |
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| 434 | DO jj = jpjm1, 2, -1 |
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| 435 | DO ji = fs_jpim1, fs_2, -1 ! vector opt. |
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| 436 | vb_ad(ji,jj,1) = vb_ad(ji,jj,1) + va_ad(ji,jj,1) |
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| 437 | va_ad(ji,jj,1) = va_ad(ji,jj,1) * p2dt |
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| 438 | END DO |
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| 439 | END DO |
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| 440 | |
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| 441 | ! 1. Vertical diffusion on u |
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| 442 | ! --------------------------- |
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| 443 | ! Matrix and second member construction |
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| 444 | ! bottom boundary condition: both zwi and zws must be masked as avmu can take |
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| 445 | ! non zero value at the ocean bottom depending on the bottom friction |
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| 446 | ! used but the bottom velocities have already been updated with the bottom |
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| 447 | ! friction velocity in dyn_bfr using values from the previous timestep. There |
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| 448 | ! is no need to include these in the implicit calculation. |
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| 449 | DO jk = 1, jpkm1 |
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| 450 | DO jj = 2, jpjm1 |
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| 451 | DO ji = fs_2, fs_jpim1 ! vector opt. |
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| 452 | zcoef = - p2dt / fse3u(ji,jj,jk) |
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| 453 | zwi(ji,jj,jk) = zcoef * avmu(ji,jj,jk ) / fse3uw(ji,jj,jk ) * umask(ji,jj,jk) |
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| 454 | zzws = zcoef * avmu(ji,jj,jk+1) / fse3uw(ji,jj,jk+1) |
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| 455 | zws(ji,jj,jk) = zzws * umask(ji,jj,jk+1) |
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| 456 | zwd(ji,jj,jk) = 1._wp - zwi(ji,jj,jk) - zzws |
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| 457 | END DO |
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| 458 | END DO |
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| 459 | END DO |
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| 460 | |
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| 461 | ! Surface boudary conditions |
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| 462 | DO jj = 2, jpjm1 |
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| 463 | DO ji = fs_2, fs_jpim1 ! vector opt. |
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| 464 | zwi(ji,jj,1) = 0._wp |
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| 465 | zwd(ji,jj,1) = 1._wp - zws(ji,jj,1) |
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| 466 | END DO |
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| 467 | END DO |
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| 468 | |
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| 469 | ! Matrix inversion starting from the first level |
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| 470 | !----------------------------------------------------------------------- |
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| 471 | ! solve m.x = y where m is a tri diagonal matrix ( jpk*jpk ) |
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| 472 | ! |
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| 473 | ! ( zwd1 zws1 0 0 0 )( zwx1 ) ( zwy1 ) |
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| 474 | ! ( zwi2 zwd2 zws2 0 0 )( zwx2 ) ( zwy2 ) |
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| 475 | ! ( 0 zwi3 zwd3 zws3 0 )( zwx3 )=( zwy3 ) |
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| 476 | ! ( ... )( ... ) ( ... ) |
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| 477 | ! ( 0 0 0 zwik zwdk )( zwxk ) ( zwyk ) |
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| 478 | ! |
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| 479 | ! m is decomposed in the product of an upper and a lower triangular matrix |
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| 480 | ! The 3 diagonal terms are in 2d arrays: zwd, zws, zwi |
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| 481 | ! The solution (the after velocity) is in ua |
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| 482 | !----------------------------------------------------------------------- |
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| 483 | |
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| 484 | ! First recurrence : Dk = Dk - Lk * Uk-1 / Dk-1 (increasing k) |
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| 485 | DO jk = 2, jpkm1 |
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| 486 | DO jj = 2, jpjm1 |
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| 487 | DO ji = fs_2, fs_jpim1 ! vector opt. |
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| 488 | 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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| 489 | END DO |
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| 490 | END DO |
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| 491 | END DO |
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| 492 | ! Normalization to obtain the general momentum trend ua |
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| 493 | DO jk = jpkm1, 1, -1 |
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| 494 | DO jj = jpjm1, 2, -1 |
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| 495 | DO ji = fs_jpim1, fs_2, -1 ! vector opt. |
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| 496 | ub_ad(ji,jj,jk) = ub_ad(ji,jj,jk) - ua_ad(ji,jj,jk) / p2dt |
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| 497 | ua_ad(ji,jj,jk) = ua_ad(ji,jj,jk) / p2dt |
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| 498 | END DO |
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| 499 | END DO |
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| 500 | END DO |
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| 501 | ! thrid recurrence : SOLk = ( Lk - Uk * Ek+1 ) / Dk |
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| 502 | DO jk = 1, jpk-2 |
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| 503 | DO jj = jpjm1, 2, -1 |
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| 504 | DO ji = fs_jpim1, fs_2, -1 ! vector opt. |
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| 505 | ua_ad(ji,jj,jk+1) = ua_ad(ji,jj,jk+1) - ua_ad(ji,jj,jk) * zws(ji,jj,jk) / zwd(ji,jj,jk) |
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| 506 | ua_ad(ji,jj,jk) = ua_ad(ji,jj,jk) / zwd(ji,jj,jk) |
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| 507 | END DO |
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| 508 | END DO |
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| 509 | END DO |
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| 510 | DO jj = jpjm1, 2, -1 |
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| 511 | DO ji = fs_jpim1, fs_2, -1 |
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| 512 | ua_ad(ji,jj,jpkm1) = ua_ad(ji,jj,jpkm1) / zwd(ji,jj,jpkm1) |
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| 513 | END DO |
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| 514 | END DO |
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| 515 | DO jk = jpkm1, 2, -1 |
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| 516 | DO jj = jpjm1, 2, -1 |
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| 517 | DO ji = fs_jpim1, fs_2, -1 ! vector opt. |
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| 518 | zrhsad = zrhsad + ua_ad(ji,jj,jk) |
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| 519 | ua_ad(ji,jj,jk-1) = ua_ad(ji,jj,jk-1) - zwi(ji,jj,jk) / zwd(ji,jj,jk-1) * ua_ad(ji,jj,jk) |
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| 520 | ua_ad(ji,jj,jk) = 0.0_wp |
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| 521 | ub_ad(ji,jj,jk) = ub_ad(ji,jj,jk) + zrhsad |
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| 522 | ua_ad(ji,jj,jk) = ua_ad(ji,jj,jk) + zrhsad * p2dt |
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| 523 | zrhsad = 0.0_wp |
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| 524 | END DO |
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| 525 | END DO |
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| 526 | END DO |
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| 527 | ! second recurrence: SOLk = RHSk - Lk / Dk-1 Lk-1 |
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| 528 | DO jj = 2, jpjm1 |
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| 529 | DO ji = fs_2, fs_jpim1 ! vector opt. |
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| 530 | ub_ad(ji,jj,1) = ub_ad(ji,jj,1) + ua_ad(ji,jj,1) |
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| 531 | ua_ad(ji,jj,1) = p2dt * ua_ad(ji,jj,1) |
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| 532 | END DO |
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| 533 | END DO |
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| 534 | |
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| 535 | |
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| 536 | |
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| 537 | END SUBROUTINE dyn_zdf_imp_adj |
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| 538 | #endif |
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| 539 | !!============================================================================== |
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| 540 | END MODULE dynzdf_imp_tam |
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