| 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 trdmod ! ocean dynamics trends |
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| 20 | USE trdmod_oce ! ocean variables trends |
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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_tsk ! 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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| 33 | !! $Header$ |
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| 34 | !! This software is governed by the CeCILL licence see modipsl/doc/NEMO_CeCILL.txt |
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| 35 | !!---------------------------------------------------------------------- |
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| 36 | |
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| 37 | CONTAINS |
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| 38 | |
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| 39 | SUBROUTINE dyn_zdf_imp_tsk( kt ) |
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| 40 | !!---------------------------------------------------------------------- |
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| 41 | !! *** ROUTINE dyn_zdf_imp_tsk *** |
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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 | !! - Save the trends in (ztdua,ztdva) ('l_trddyn') |
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| 58 | !! |
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| 59 | !! History : |
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| 60 | !! 8.5 ! 02-08 (G. Madec) auto-tasking option |
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| 61 | !! 9.0 ! 04-08 (C. Talandier) New trends organization |
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| 62 | !!--------------------------------------------------------------------- |
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| 63 | !! * Modules used |
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| 64 | USE oce, ONLY : ztdua => ta, & ! use ta as 3D workspace |
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| 65 | ztdva => sa ! use sa as 3D workspace |
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| 66 | |
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| 67 | !! * Arguments |
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| 68 | INTEGER, INTENT( in ) :: kt ! ocean time-step index |
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| 69 | |
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| 70 | !! * Local declarations |
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| 71 | INTEGER :: ji, jj, jk ! dummy loop indices |
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| 72 | INTEGER :: & |
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| 73 | ikst, ikenm2, ikstp1, & ! temporary integers |
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| 74 | ikbu, ikbum1, ikbv, ikbvm1 ! " " |
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| 75 | REAL(wp) :: & |
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| 76 | zrau0r, z2dt, zua, zva, & !temporary scalars |
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| 77 | z2dtf, zcoef, zzws |
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| 78 | REAL(wp), DIMENSION(jpi,jpk) :: & |
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| 79 | zwx, zwy, zwz, & ! workspace |
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| 80 | zwd, zws, zwi, zwt |
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| 81 | REAL(wp), DIMENSION(jpi,jpj) :: & |
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| 82 | ztsx, ztsy, ztbx, ztby ! temporary workspace arrays |
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| 83 | !!---------------------------------------------------------------------- |
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| 84 | |
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| 85 | IF( kt == nit000 ) THEN |
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| 86 | IF(lwp) WRITE(numout,*) |
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| 87 | IF(lwp) WRITE(numout,*) 'dyn_zdf_imp_tsk : vertical momentum diffusion implicit operator' |
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| 88 | IF(lwp) WRITE(numout,*) '~~~~~~~~~~~~~~~ auto-task case (j-k-i loop)' |
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| 89 | ENDIF |
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| 90 | |
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| 91 | |
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| 92 | ! 0. Local constant initialization |
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| 93 | ! -------------------------------- |
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| 94 | zrau0r = 1. / rau0 ! inverse of the reference density |
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| 95 | z2dt = 2. * rdt ! Leap-frog environnement |
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| 96 | ztsx(:,:) = 0.e0 |
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| 97 | ztsy(:,:) = 0.e0 |
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| 98 | ztbx(:,:) = 0.e0 |
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| 99 | ztby(:,:) = 0.e0 |
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| 100 | ! Euler time stepping when starting from rest |
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| 101 | IF( neuler == 0 .AND. kt == nit000 ) z2dt = rdt |
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| 102 | |
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| 103 | ! Save ua and va trends |
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| 104 | IF( l_trddyn ) THEN |
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| 105 | ztdua(:,:,:) = ua(:,:,:) |
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| 106 | ztdva(:,:,:) = va(:,:,:) |
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| 107 | ENDIF |
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| 108 | |
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| 109 | ! ! =============== |
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| 110 | DO jj = 2, jpjm1 ! Vertical slab |
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| 111 | ! ! =============== |
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| 112 | ! 1. Vertical diffusion on u |
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| 113 | ! --------------------------- |
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| 114 | |
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| 115 | ! Matrix and second member construction |
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| 116 | ! bottom boundary condition: only zws must be masked as avmu can take |
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| 117 | ! non zero value at the ocean bottom depending on the bottom friction |
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| 118 | ! used (see zdfmix.F) |
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| 119 | DO jk = 1, jpkm1 |
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| 120 | DO ji = 2, jpim1 |
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| 121 | zcoef = - z2dt / fse3u(ji,jj,jk) |
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| 122 | zwi(ji,jk) = zcoef * avmu(ji,jj,jk ) / fse3uw(ji,jj,jk ) |
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| 123 | zzws = zcoef * avmu(ji,jj,jk+1) / fse3uw(ji,jj,jk+1) |
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| 124 | zws(ji,jk) = zzws * umask(ji,jj,jk+1) |
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| 125 | zwd(ji,jk) = 1. - zwi(ji,jk) - zzws |
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| 126 | zwy(ji,jk) = ub(ji,jj,jk) + z2dt * ua(ji,jj,jk) |
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| 127 | END DO |
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| 128 | END DO |
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| 129 | |
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| 130 | ! Surface boudary conditions |
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| 131 | DO ji = 2, jpim1 |
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| 132 | z2dtf = z2dt / ( fse3u(ji,jj,1)*rau0 ) |
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| 133 | zwi(ji,1) = 0. |
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| 134 | zwd(ji,1) = 1. - zws(ji,1) |
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| 135 | zwy(ji,1) = zwy(ji,1) + z2dtf * taux(ji,jj) |
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| 136 | END DO |
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| 137 | |
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| 138 | ! Matrix inversion starting from the first level |
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| 139 | ikst = 1 |
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| 140 | !!---------------------------------------------------------------------- |
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| 141 | !! ZDF.MATRIXSOLVER |
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| 142 | !! ******************** |
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| 143 | !!---------------------------------------------------------------------- |
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| 144 | !! Matrix inversion |
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| 145 | ! solve m.x = y where m is a tri diagonal matrix ( jpk*jpk ) |
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| 146 | ! |
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| 147 | ! ( zwd1 zws1 0 0 0 )( zwx1 ) ( zwy1 ) |
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| 148 | ! ( zwi2 zwd2 zws2 0 0 )( zwx2 ) ( zwy2 ) |
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| 149 | ! ( 0 zwi3 zwd3 zws3 0 )( zwx3 )=( zwy3 ) |
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| 150 | ! ( ... )( ... ) ( ... ) |
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| 151 | ! ( 0 0 0 zwik zwdk )( zwxk ) ( zwyk ) |
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| 152 | ! |
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| 153 | ! m is decomposed in the product of an upper and lower triangular |
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| 154 | ! matrix |
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| 155 | ! The 3 diagonal terms are in 2d arrays: zwd, zws, zwi |
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| 156 | ! The second member is in 2d array zwy |
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| 157 | ! The solution is in 2d array zwx |
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| 158 | ! The 2d arry zwt and zwz are work space arrays |
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| 159 | ! |
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| 160 | ! N.B. the starting vertical index (ikst) is equal to 1 except for |
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| 161 | ! the resolution of tke matrix where surface tke value is prescribed |
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| 162 | ! so that ikstrt=2. |
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| 163 | !!---------------------------------------------------------------------- |
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| 164 | |
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| 165 | ikstp1 = ikst + 1 |
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| 166 | ikenm2 = jpk - 2 |
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| 167 | DO ji = 2, jpim1 |
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| 168 | zwt(ji,ikst) = zwd(ji,ikst) |
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| 169 | END DO |
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| 170 | DO jk = ikstp1, jpkm1 |
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| 171 | DO ji = 2, jpim1 |
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| 172 | zwt(ji,jk) = zwd(ji,jk) - zwi(ji,jk) * zws(ji,jk-1) / zwt(ji,jk-1) |
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| 173 | END DO |
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| 174 | END DO |
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| 175 | DO ji = 2, jpim1 |
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| 176 | zwz(ji,ikst) = zwy(ji,ikst) |
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| 177 | END DO |
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| 178 | DO jk = ikstp1, jpkm1 |
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| 179 | DO ji = 2, jpim1 |
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| 180 | zwz(ji,jk) = zwy(ji,jk) - zwi(ji,jk) / zwt(ji,jk-1) * zwz(ji,jk-1) |
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| 181 | END DO |
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| 182 | END DO |
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| 183 | DO ji = 2, jpim1 |
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| 184 | zwx(ji,jpkm1) = zwz(ji,jpkm1) / zwt(ji,jpkm1) |
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| 185 | END DO |
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| 186 | DO jk = ikenm2, ikst, -1 |
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| 187 | DO ji = 2, jpim1 |
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| 188 | zwx(ji,jk) =( zwz(ji,jk) - zws(ji,jk) * zwx(ji,jk+1) ) / zwt(ji,jk) |
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| 189 | END DO |
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| 190 | END DO |
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| 191 | |
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| 192 | ! Normalization to obtain the general momentum trend ua |
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| 193 | DO jk = 1, jpkm1 |
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| 194 | DO ji = 2, jpim1 |
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| 195 | ua(ji,jj,jk) = ( zwx(ji,jk) - ub(ji,jj,jk) ) / z2dt |
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| 196 | END DO |
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| 197 | END DO |
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| 198 | |
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| 199 | ! diagnose surface and bottom momentum fluxes |
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| 200 | ! for trends diagnostics |
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| 201 | DO ji = 2, jpim1 |
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| 202 | ! save the surface forcing momentum fluxes |
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| 203 | ztsx(ji,jj) = taux(ji,jj) / ( fse3u(ji,jj,1)*rau0 ) |
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| 204 | ! save bottom friction momentum fluxes |
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| 205 | ikbu = MIN( mbathy(ji+1,jj), mbathy(ji,jj) ) |
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| 206 | ikbum1 = MAX( ikbu-1, 1 ) |
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| 207 | ztbx(ji,jj) = - avmu(ji,jj,ikbu) * zwx(ji,ikbum1) & |
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| 208 | / ( fse3u(ji,jj,ikbum1)*fse3uw(ji,jj,ikbu) ) |
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| 209 | ! subtract surface forcing and bottom friction trend from vertical |
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| 210 | ! diffusive momentum trend |
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| 211 | ztdua(ji,jj,1 ) = ztdua(ji,jj,1 ) - ztsx(ji,jj) |
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| 212 | ztdua(ji,jj,ikbum1) = ztdua(ji,jj,ikbum1) - ztbx(ji,jj) |
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| 213 | END DO |
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| 214 | |
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| 215 | ! 2. Vertical diffusion on v |
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| 216 | ! --------------------------- |
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| 217 | |
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| 218 | ! Matrix and second member construction |
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| 219 | ! bottom boundary condition: only zws must be masked as avmv can take |
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| 220 | ! non zero value at the ocean bottom depending on the bottom friction |
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| 221 | ! used (see zdfmix.F) |
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| 222 | DO jk = 1, jpkm1 |
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| 223 | DO ji = 2, jpim1 |
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| 224 | zcoef = -z2dt/fse3v(ji,jj,jk) |
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| 225 | zwi(ji,jk) = zcoef * avmv(ji,jj,jk ) / fse3vw(ji,jj,jk ) |
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| 226 | zzws = zcoef * avmv(ji,jj,jk+1) / fse3vw(ji,jj,jk+1) |
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| 227 | zws(ji,jk) = zzws * vmask(ji,jj,jk+1) |
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| 228 | zwd(ji,jk) = 1. - zwi(ji,jk) - zzws |
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| 229 | zwy(ji,jk) = vb(ji,jj,jk) + z2dt * va(ji,jj,jk) |
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| 230 | END DO |
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| 231 | END DO |
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| 232 | |
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| 233 | ! Surface boudary conditions |
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| 234 | DO ji = 2, jpim1 |
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| 235 | z2dtf = z2dt / ( fse3v(ji,jj,1)*rau0 ) |
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| 236 | zwi(ji,1) = 0.e0 |
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| 237 | zwd(ji,1) = 1. - zws(ji,1) |
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| 238 | zwy(ji,1) = zwy(ji,1) + z2dtf * tauy(ji,jj) |
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| 239 | END DO |
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| 240 | |
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| 241 | ! Matrix inversion starting from the first level |
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| 242 | ikst = 1 |
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| 243 | !!---------------------------------------------------------------------- |
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| 244 | !! ZDF.MATRIXSOLVER |
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| 245 | !! ******************** |
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| 246 | !!---------------------------------------------------------------------- |
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| 247 | !! Matrix inversion |
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| 248 | ! solve m.x = y where m is a tri diagonal matrix ( jpk*jpk ) |
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| 249 | ! |
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| 250 | ! ( zwd1 zws1 0 0 0 )( zwx1 ) ( zwy1 ) |
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| 251 | ! ( zwi2 zwd2 zws2 0 0 )( zwx2 ) ( zwy2 ) |
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| 252 | ! ( 0 zwi3 zwd3 zws3 0 )( zwx3 )=( zwy3 ) |
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| 253 | ! ( ... )( ... ) ( ... ) |
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| 254 | ! ( 0 0 0 zwik zwdk )( zwxk ) ( zwyk ) |
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| 255 | ! |
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| 256 | ! m is decomposed in the product of an upper and lower triangular |
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| 257 | ! matrix |
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| 258 | ! The 3 diagonal terms are in 2d arrays: zwd, zws, zwi |
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| 259 | ! The second member is in 2d array zwy |
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| 260 | ! The solution is in 2d array zwx |
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| 261 | ! The 2d arry zwt and zwz are work space arrays |
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| 262 | ! |
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| 263 | ! N.B. the starting vertical index (ikst) is equal to 1 except for |
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| 264 | ! the resolution of tke matrix where surface tke value is prescribed |
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| 265 | ! so that ikstrt=2. |
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| 266 | !!---------------------------------------------------------------------- |
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| 267 | |
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| 268 | ikstp1 = ikst + 1 |
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| 269 | ikenm2 = jpk - 2 |
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| 270 | DO ji = 2, jpim1 |
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| 271 | zwt(ji,ikst) = zwd(ji,ikst) |
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| 272 | END DO |
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| 273 | DO jk = ikstp1, jpkm1 |
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| 274 | DO ji = 2, jpim1 |
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| 275 | zwt(ji,jk) = zwd(ji,jk) - zwi(ji,jk) * zws(ji,jk-1) / zwt(ji,jk-1) |
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| 276 | END DO |
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| 277 | END DO |
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| 278 | DO ji = 2, jpim1 |
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| 279 | zwz(ji,ikst) = zwy(ji,ikst) |
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| 280 | END DO |
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| 281 | DO jk = ikstp1, jpkm1 |
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| 282 | DO ji = 2, jpim1 |
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| 283 | zwz(ji,jk) = zwy(ji,jk) - zwi(ji,jk) / zwt(ji,jk-1) * zwz(ji,jk-1) |
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| 284 | END DO |
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| 285 | END DO |
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| 286 | DO ji = 2, jpim1 |
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| 287 | zwx(ji,jpkm1) = zwz(ji,jpkm1) / zwt(ji,jpkm1) |
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| 288 | END DO |
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| 289 | DO jk = ikenm2, ikst, -1 |
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| 290 | DO ji = 2, jpim1 |
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| 291 | zwx(ji,jk) =( zwz(ji,jk) - zws(ji,jk) * zwx(ji,jk+1) ) / zwt(ji,jk) |
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| 292 | END DO |
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| 293 | END DO |
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| 294 | |
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| 295 | ! Normalization to obtain the general momentum trend va |
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| 296 | DO jk = 1, jpkm1 |
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| 297 | DO ji = 2, jpim1 |
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| 298 | va(ji,jj,jk) = ( zwx(ji,jk) - vb(ji,jj,jk) ) / z2dt |
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| 299 | END DO |
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| 300 | END DO |
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| 301 | |
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| 302 | ! diagnose surface and bottom momentum fluxes |
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| 303 | ! for trends diagnostics |
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| 304 | DO ji = 2, jpim1 |
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| 305 | ! save the surface forcing momentum fluxes |
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| 306 | ztsy(ji,jj) = tauy(ji,jj) / ( fse3v(ji,jj,1)*rau0 ) |
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| 307 | ! save bottom friction momentum fluxes |
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| 308 | ikbv = MIN( mbathy(ji,jj+1), mbathy(ji,jj) ) |
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| 309 | ikbvm1 = MAX( ikbv-1, 1 ) |
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| 310 | ztby(ji,jj) = - avmv(ji,jj,ikbv) * zwx(ji,ikbvm1) & |
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| 311 | / ( fse3v(ji,jj,ikbvm1)*fse3vw(ji,jj,ikbv) ) |
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| 312 | ! subtract surface forcing and bottom friction trend from vertical |
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| 313 | ! diffusive momentum trend |
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| 314 | ztdva(ji,jj,1 ) = ztdva(ji,jj,1 ) - ztsy(ji,jj) |
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| 315 | ztdva(ji,jj,ikbvm1) = ztdva(ji,jj,ikbvm1) - ztby(ji,jj) |
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| 316 | END DO |
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| 317 | ! ! =============== |
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| 318 | END DO ! End of slab |
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| 319 | ! ! =============== |
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| 320 | |
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| 321 | ! save the vertical diffusion trends for diagnostic |
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| 322 | ! momentum trends |
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| 323 | IF( l_trddyn ) THEN |
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| 324 | ztdua(:,:,:) = ua(:,:,:) - ztdua(:,:,:) |
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| 325 | ztdva(:,:,:) = va(:,:,:) - ztdva(:,:,:) |
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| 326 | |
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| 327 | CALL trd_mod(ztdua, ztdva, jpdtdzdf, 'DYN', kt) |
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| 328 | ztdua(:,:,:) = 0.e0 |
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| 329 | ztdva(:,:,:) = 0.e0 |
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| 330 | ztdua(:,:,1) = ztsx(:,:) |
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| 331 | ztdva(:,:,1) = ztsy(:,:) |
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| 332 | CALL trd_mod(ztdua , ztdva , jpdtdswf, 'DYN', kt) |
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| 333 | ztdua(:,:,:) = 0.e0 |
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| 334 | ztdva(:,:,:) = 0.e0 |
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| 335 | ztdua(:,:,1) = ztbx(:,:) |
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| 336 | ztdva(:,:,1) = ztby(:,:) |
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| 337 | CALL trd_mod(ztdua , ztdva , jpdtdbfr, 'DYN', kt) |
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| 338 | ENDIF |
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| 339 | |
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| 340 | IF(l_ctl) THEN ! print sum trends (used for debugging) |
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| 341 | zua = SUM( ua(2:nictl,2:njctl,1:jpkm1) * umask(2:nictl,2:njctl,1:jpkm1) ) |
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| 342 | zva = SUM( va(2:nictl,2:njctl,1:jpkm1) * vmask(2:nictl,2:njctl,1:jpkm1) ) |
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| 343 | WRITE(numout,*) ' zdf - Ua: ', zua-u_ctl, ' Va: ', zva-v_ctl |
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| 344 | u_ctl = zua ; v_ctl = zva |
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| 345 | ENDIF |
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| 346 | |
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| 347 | END SUBROUTINE dyn_zdf_imp_tsk |
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| 348 | |
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| 349 | !!============================================================================== |
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| 350 | END MODULE dynzdf_imp_atsk |
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