| 1 | MODULE dynzdf_imp_atsk |
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| 2 | !!============================================================================== |
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| 3 | !! *** MODULE dynzdf_imp_atsk *** |
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| 4 | !! Ocean dynamics: vertical component(s) of the momentum mixing trend |
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| 5 | !!============================================================================== |
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| 6 | |
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| 7 | !!---------------------------------------------------------------------- |
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| 8 | !! dyn_zdf_imp_tsk : update the momentum trend with the vertical |
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| 9 | !! diffusion using an implicit time-stepping and |
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| 10 | !! j-k-i loops. |
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| 11 | !!---------------------------------------------------------------------- |
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| 12 | !! * Modules used |
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| 13 | USE oce ! ocean dynamics and tracers |
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| 14 | USE dom_oce ! ocean space and time domain |
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| 15 | USE phycst ! physical constants |
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| 16 | USE zdf_oce ! ocean vertical physics |
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| 17 | USE in_out_manager ! I/O manager |
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| 18 | USE taumod ! surface ocean stress |
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| 19 | USE trddyn_oce ! dynamics trends diagnostics variables |
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| 20 | |
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| 21 | IMPLICIT NONE |
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| 22 | PRIVATE |
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| 23 | |
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| 24 | !! * Routine accessibility |
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| 25 | PUBLIC dyn_zdf_imp_tsk ! called by step.F90 |
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| 26 | |
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| 27 | !! * Substitutions |
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| 28 | # include "domzgr_substitute.h90" |
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| 29 | # include "vectopt_loop_substitute.h90" |
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| 30 | !!---------------------------------------------------------------------- |
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| 31 | !! OPA 9.0 , LODYC-IPSL (2003) |
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| 32 | !!---------------------------------------------------------------------- |
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| 33 | |
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| 34 | CONTAINS |
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| 35 | |
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| 36 | SUBROUTINE dyn_zdf_imp_tsk( kt ) |
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| 37 | !!---------------------------------------------------------------------- |
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| 38 | !! *** ROUTINE dyn_zdf_imp_tsk *** |
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| 39 | !! |
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| 40 | !! ** Purpose : Compute the trend due to the vert. momentum diffusion |
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| 41 | !! and the surface forcing, and add it to the general trend of |
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| 42 | !! the momentum equations. |
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| 43 | !! |
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| 44 | !! ** Method : The vertical momentum mixing trend is given by : |
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| 45 | !! dz( avmu dz(u) ) = 1/e3u dk+1( avmu/e3uw dk(ua) ) |
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| 46 | !! backward time stepping |
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| 47 | !! Surface boundary conditions: wind stress input |
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| 48 | !! Bottom boundary conditions : bottom stress (cf zdfbfr.F) |
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| 49 | !! Add this trend to the general trend ua : |
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| 50 | !! ua = ua + dz( avmu dz(u) ) |
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| 51 | !! |
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| 52 | !! ** Action : - Update (ua,va) arrays with the after vertical diffusive |
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| 53 | !! mixing trend. |
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| 54 | !! - Save the trends in (utrd,vtrd) ('key_diatrends') |
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| 55 | !! |
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| 56 | !! History : |
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| 57 | !! 8.5 ! 02-08 (G. Madec) auto-tasking option |
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| 58 | !!--------------------------------------------------------------------- |
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| 59 | !! * Arguments |
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| 60 | INTEGER, INTENT( in ) :: kt ! ocean time-step index |
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| 61 | |
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| 62 | !! * Local declarations |
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| 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) :: & |
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| 66 | zrau0r, z2dt, zua, zva, & ! temporary scalars |
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| 67 | z2dtf, zcoef, zzws |
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| 68 | REAL(wp), DIMENSION(jpi,jpk) :: & |
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| 69 | zwx, zwy, zwz, & ! workspace |
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| 70 | zwd, zws, zwi, zwt |
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| 71 | #if defined key_trddyn |
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| 72 | INTEGER :: & |
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| 73 | ikbu, ikbum1, ikbv, ikbvm1 & ! temporary integers |
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| 74 | #endif |
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| 75 | !!---------------------------------------------------------------------- |
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| 76 | |
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| 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_tsk : vertical momentum diffusion implicit operator' |
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| 80 | IF(lwp) WRITE(numout,*) '~~~~~~~~~~~~~~~ auto-task case (j-k-i loop)' |
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| 81 | ENDIF |
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| 82 | |
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| 83 | |
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| 84 | ! 0. Local constant initialization |
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| 85 | ! -------------------------------- |
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| 86 | zrau0r = 1. / rau0 ! inverse of the reference density |
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| 87 | z2dt = 2. * rdt ! Leap-frog environnement |
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| 88 | ! Euler time stepping when starting from rest |
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| 89 | IF( neuler == 0 .AND. kt == nit000 ) z2dt = rdt |
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| 90 | |
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| 91 | ! ! =============== |
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| 92 | DO jj = 2, jpjm1 ! Vertical slab |
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| 93 | ! ! =============== |
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| 94 | ! 1. Vertical diffusion on u |
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| 95 | ! --------------------------- |
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| 96 | |
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| 97 | ! Matrix and second member construction |
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| 98 | ! bottom boundary condition: only zws must be masked as avmu can take |
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| 99 | ! non zero value at the ocean bottom depending on the bottom friction |
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| 100 | ! used (see zdfmix.F) |
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| 101 | DO jk = 1, jpkm1 |
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| 102 | DO ji = 2, jpim1 |
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| 103 | zcoef = - z2dt / fse3u(ji,jj,jk) |
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| 104 | zwi(ji,jk) = zcoef * avmu(ji,jj,jk ) / fse3uw(ji,jj,jk ) |
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| 105 | zzws = zcoef * avmu(ji,jj,jk+1) / fse3uw(ji,jj,jk+1) |
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| 106 | zws(ji,jk) = zzws * umask(ji,jj,jk+1) |
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| 107 | zwd(ji,jk) = 1. - zwi(ji,jk) - zzws |
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| 108 | zwy(ji,jk) = ub(ji,jj,jk) + z2dt * ua(ji,jj,jk) |
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| 109 | END DO |
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| 110 | END DO |
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| 111 | |
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| 112 | ! Surface boudary conditions |
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| 113 | DO ji = 2, jpim1 |
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| 114 | z2dtf = z2dt / ( fse3u(ji,jj,1)*rau0 ) |
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| 115 | zwi(ji,1) = 0. |
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| 116 | zwd(ji,1) = 1. - zws(ji,1) |
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| 117 | zwy(ji,1) = zwy(ji,1) + z2dtf * taux(ji,jj) |
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| 118 | END DO |
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| 119 | |
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| 120 | ! Matrix inversion starting from the first level |
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| 121 | ikst = 1 |
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| 122 | !!---------------------------------------------------------------------- |
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| 123 | !! ZDF.MATRIXSOLVER |
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| 124 | !! ******************** |
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| 125 | !!---------------------------------------------------------------------- |
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| 126 | !! Matrix inversion |
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| 127 | ! solve m.x = y where m is a tri diagonal matrix ( jpk*jpk ) |
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| 128 | ! |
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| 129 | ! ( zwd1 zws1 0 0 0 )( zwx1 ) ( zwy1 ) |
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| 130 | ! ( zwi2 zwd2 zws2 0 0 )( zwx2 ) ( zwy2 ) |
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| 131 | ! ( 0 zwi3 zwd3 zws3 0 )( zwx3 )=( zwy3 ) |
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| 132 | ! ( ... )( ... ) ( ... ) |
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| 133 | ! ( 0 0 0 zwik zwdk )( zwxk ) ( zwyk ) |
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| 134 | ! |
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| 135 | ! m is decomposed in the product of an upper and lower triangular |
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| 136 | ! matrix |
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| 137 | ! The 3 diagonal terms are in 2d arrays: zwd, zws, zwi |
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| 138 | ! The second member is in 2d array zwy |
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| 139 | ! The solution is in 2d array zwx |
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| 140 | ! The 2d arry zwt and zwz are work space arrays |
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| 141 | ! |
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| 142 | ! N.B. the starting vertical index (ikst) is equal to 1 except for |
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| 143 | ! the resolution of tke matrix where surface tke value is prescribed |
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| 144 | ! so that ikstrt=2. |
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| 145 | !!---------------------------------------------------------------------- |
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| 146 | |
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| 147 | ikstp1 = ikst + 1 |
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| 148 | ikenm2 = jpk - 2 |
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| 149 | DO ji = 2, jpim1 |
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| 150 | zwt(ji,ikst) = zwd(ji,ikst) |
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| 151 | END DO |
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| 152 | DO jk = ikstp1, jpkm1 |
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| 153 | DO ji = 2, jpim1 |
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| 154 | zwt(ji,jk) = zwd(ji,jk) - zwi(ji,jk) * zws(ji,jk-1) / zwt(ji,jk-1) |
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| 155 | END DO |
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| 156 | END DO |
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| 157 | DO ji = 2, jpim1 |
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| 158 | zwz(ji,ikst) = zwy(ji,ikst) |
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| 159 | END DO |
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| 160 | DO jk = ikstp1, jpkm1 |
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| 161 | DO ji = 2, jpim1 |
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| 162 | zwz(ji,jk) = zwy(ji,jk) - zwi(ji,jk) / zwt(ji,jk-1) * zwz(ji,jk-1) |
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| 163 | END DO |
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| 164 | END DO |
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| 165 | DO ji = 2, jpim1 |
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| 166 | zwx(ji,jpkm1) = zwz(ji,jpkm1) / zwt(ji,jpkm1) |
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| 167 | END DO |
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| 168 | DO jk = ikenm2, ikst, -1 |
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| 169 | DO ji = 2, jpim1 |
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| 170 | zwx(ji,jk) =( zwz(ji,jk) - zws(ji,jk) * zwx(ji,jk+1) ) / zwt(ji,jk) |
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| 171 | END DO |
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| 172 | END DO |
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| 173 | |
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| 174 | ! Normalization to obtain the general momentum trend ua |
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| 175 | DO jk = 1, jpkm1 |
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| 176 | DO ji = 2, jpim1 |
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| 177 | zua = ( zwx(ji,jk) - ub(ji,jj,jk) ) / z2dt |
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| 178 | #if defined key_trddyn |
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| 179 | ! save the vertical diffusive momentum trend |
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| 180 | utrd(ji,jj,jk,7) = zua - ua(ji,jj,jk) |
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| 181 | #endif |
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| 182 | ua(ji,jj,jk) = zua |
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| 183 | END DO |
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| 184 | END DO |
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| 185 | |
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| 186 | #if defined key_trddyn |
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| 187 | ! diagnose surface and bottom momentum fluxes |
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| 188 | DO ji = 2, jpim1 |
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| 189 | ! save the surface forcing momentum fluxes |
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| 190 | tautrd(ji,jj,1) = taux(ji,jj) / ( fse3u(ji,jj,1)*rau0 ) |
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| 191 | ! save bottom friction momentum fluxes |
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| 192 | ikbu = MIN( mbathy(ji+1,jj), mbathy(ji,jj) ) |
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| 193 | ikbum1 = MAX( ikbu-1, 1 ) |
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| 194 | tautrd(ji,jj,3) = - avmu(ji,jj,ikbu) * zwx(ji,ikbum1) & |
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| 195 | / ( fse3u(ji,jj,ikbum1)*fse3uw(ji,jj,ikbu) ) |
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| 196 | ! subtract surface forcing and bottom friction trend from vertical |
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| 197 | ! diffusive momentum trend |
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| 198 | utrd(ji,jj,1 ,7) = utrd(ji,jj,1 ,7) - tautrd(ji,jj,1) |
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| 199 | utrd(ji,jj,ikbum1,7) = utrd(ji,jj,ikbum1,7) - tautrd(ji,jj,3) |
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| 200 | END DO |
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| 201 | #endif |
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| 202 | |
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| 203 | ! 2. Vertical diffusion on v |
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| 204 | ! --------------------------- |
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| 205 | |
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| 206 | ! Matrix and second member construction |
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| 207 | ! bottom boundary condition: only zws must be masked as avmv can take |
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| 208 | ! non zero value at the ocean bottom depending on the bottom friction |
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| 209 | ! used (see zdfmix.F) |
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| 210 | DO jk = 1, jpkm1 |
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| 211 | DO ji = 2, jpim1 |
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| 212 | zcoef = -z2dt/fse3v(ji,jj,jk) |
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| 213 | zwi(ji,jk) = zcoef * avmv(ji,jj,jk ) / fse3vw(ji,jj,jk ) |
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| 214 | zzws = zcoef * avmv(ji,jj,jk+1) / fse3vw(ji,jj,jk+1) |
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| 215 | zws(ji,jk) = zzws * vmask(ji,jj,jk+1) |
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| 216 | zwd(ji,jk) = 1. - zwi(ji,jk) - zzws |
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| 217 | zwy(ji,jk) = vb(ji,jj,jk) + z2dt * va(ji,jj,jk) |
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| 218 | END DO |
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| 219 | END DO |
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| 220 | |
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| 221 | ! Surface boudary conditions |
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| 222 | DO ji = 2, jpim1 |
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| 223 | z2dtf = z2dt / ( fse3v(ji,jj,1)*rau0 ) |
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| 224 | zwi(ji,1) = 0.e0 |
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| 225 | zwd(ji,1) = 1. - zws(ji,1) |
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| 226 | zwy(ji,1) = zwy(ji,1) + z2dtf * tauy(ji,jj) |
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| 227 | END DO |
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| 228 | |
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| 229 | ! Matrix inversion starting from the first level |
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| 230 | ikst = 1 |
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| 231 | !!---------------------------------------------------------------------- |
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| 232 | !! ZDF.MATRIXSOLVER |
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| 233 | !! ******************** |
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| 234 | !!---------------------------------------------------------------------- |
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| 235 | !! Matrix inversion |
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| 236 | ! solve m.x = y where m is a tri diagonal matrix ( jpk*jpk ) |
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| 237 | ! |
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| 238 | ! ( zwd1 zws1 0 0 0 )( zwx1 ) ( zwy1 ) |
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| 239 | ! ( zwi2 zwd2 zws2 0 0 )( zwx2 ) ( zwy2 ) |
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| 240 | ! ( 0 zwi3 zwd3 zws3 0 )( zwx3 )=( zwy3 ) |
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| 241 | ! ( ... )( ... ) ( ... ) |
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| 242 | ! ( 0 0 0 zwik zwdk )( zwxk ) ( zwyk ) |
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| 243 | ! |
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| 244 | ! m is decomposed in the product of an upper and lower triangular |
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| 245 | ! matrix |
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| 246 | ! The 3 diagonal terms are in 2d arrays: zwd, zws, zwi |
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| 247 | ! The second member is in 2d array zwy |
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| 248 | ! The solution is in 2d array zwx |
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| 249 | ! The 2d arry zwt and zwz are work space arrays |
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| 250 | ! |
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| 251 | ! N.B. the starting vertical index (ikst) is equal to 1 except for |
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| 252 | ! the resolution of tke matrix where surface tke value is prescribed |
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| 253 | ! so that ikstrt=2. |
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| 254 | !!---------------------------------------------------------------------- |
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| 255 | |
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| 256 | ikstp1 = ikst + 1 |
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| 257 | ikenm2 = jpk - 2 |
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| 258 | DO ji = 2, jpim1 |
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| 259 | zwt(ji,ikst) = zwd(ji,ikst) |
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| 260 | END DO |
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| 261 | DO jk = ikstp1, jpkm1 |
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| 262 | DO ji = 2, jpim1 |
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| 263 | zwt(ji,jk) = zwd(ji,jk) - zwi(ji,jk) * zws(ji,jk-1) / zwt(ji,jk-1) |
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| 264 | END DO |
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| 265 | END DO |
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| 266 | DO ji = 2, jpim1 |
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| 267 | zwz(ji,ikst) = zwy(ji,ikst) |
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| 268 | END DO |
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| 269 | DO jk = ikstp1, jpkm1 |
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| 270 | DO ji = 2, jpim1 |
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| 271 | zwz(ji,jk) = zwy(ji,jk) - zwi(ji,jk) / zwt(ji,jk-1) * zwz(ji,jk-1) |
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| 272 | END DO |
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| 273 | END DO |
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| 274 | DO ji = 2, jpim1 |
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| 275 | zwx(ji,jpkm1) = zwz(ji,jpkm1) / zwt(ji,jpkm1) |
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| 276 | END DO |
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| 277 | DO jk = ikenm2, ikst, -1 |
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| 278 | DO ji = 2, jpim1 |
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| 279 | zwx(ji,jk) =( zwz(ji,jk) - zws(ji,jk) * zwx(ji,jk+1) ) / zwt(ji,jk) |
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| 280 | END DO |
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| 281 | END DO |
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| 282 | |
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| 283 | ! Normalization to obtain the general momentum trend va |
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| 284 | DO jk = 1, jpkm1 |
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| 285 | DO ji = 2, jpim1 |
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| 286 | zva = ( zwx(ji,jk) - vb(ji,jj,jk) ) / z2dt |
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| 287 | #if defined key_trddyn |
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| 288 | ! save the vertical diffusive momentum fluxes |
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| 289 | vtrd(ji,jj,jk,7) = zva - va(ji,jj,jk) |
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| 290 | #endif |
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| 291 | va(ji,jj,jk) = zva |
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| 292 | END DO |
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| 293 | END DO |
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| 294 | |
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| 295 | #if defined key_trddyn |
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| 296 | ! diagnose surface and bottom momentum fluxes |
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| 297 | DO ji = 2, jpim1 |
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| 298 | ! save the surface forcing momentum fluxes |
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| 299 | tautrd(ji,jj,2) = tauy(ji,jj) / ( fse3v(ji,jj,1)*rau0 ) |
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| 300 | ! save bottom friction momentum fluxes |
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| 301 | ikbv = MIN( mbathy(ji,jj+1), mbathy(ji,jj) ) |
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| 302 | ikbvm1 = MAX( ikbv-1, 1 ) |
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| 303 | tautrd(ji,jj,4) = - avmv(ji,jj,ikbv) * zwx(ji,ikbvm1) & |
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| 304 | / ( fse3v(ji,jj,ikbvm1)*fse3vw(ji,jj,ikbv) ) |
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| 305 | ! subtract surface forcing and bottom friction trend from vertical |
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| 306 | ! diffusive momentum trend |
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| 307 | vtrd(ji,jj,1 ,7) = vtrd(ji,jj,1 ,7) - tautrd(ji,jj,2) |
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| 308 | vtrd(ji,jj,ikbvm1,7) = vtrd(ji,jj,ikbvm1,7) - tautrd(ji,jj,4) |
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| 309 | END DO |
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| 310 | #endif |
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| 311 | ! ! =============== |
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| 312 | END DO ! End of slab |
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| 313 | ! ! =============== |
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| 314 | END SUBROUTINE dyn_zdf_imp_tsk |
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| 315 | |
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| 316 | !!============================================================================== |
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| 317 | END MODULE dynzdf_imp_atsk |
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