| 1 | MODULE dynzdf |
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| 2 | !!============================================================================== |
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| 3 | !! *** MODULE dynzdf *** |
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| 4 | !! Ocean dynamics : vertical component of the momentum mixing trend |
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| 5 | !!============================================================================== |
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| 6 | !! History : 1.0 ! 2005-11 (G. Madec) Original code |
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| 7 | !! 3.3 ! 2010-10 (C. Ethe, G. Madec) reorganisation of initialisation phase |
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| 8 | !! 4.0 ! 2017-06 (G. Madec) remove the explicit time-stepping option + avm at t-point |
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| 9 | !!---------------------------------------------------------------------- |
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| 10 | |
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| 11 | !!---------------------------------------------------------------------- |
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| 12 | !! dyn_zdf : compute the after velocity through implicit calculation of vertical mixing |
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| 13 | !!---------------------------------------------------------------------- |
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| 14 | USE oce ! ocean dynamics and tracers variables |
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| 15 | USE phycst ! physical constants |
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| 16 | USE dom_oce ! ocean space and time domain variables |
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| 17 | USE sbc_oce ! surface boundary condition: ocean |
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| 18 | USE zdf_oce ! ocean vertical physics variables |
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| 19 | USE zdfdrg ! vertical physics: top/bottom drag coef. |
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| 20 | USE dynadv ,ONLY: ln_dynadv_vec ! dynamics: advection form |
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| 21 | #if defined key_loop_fusion |
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| 22 | USE dynldf_iso_lf,ONLY: akzu, akzv ! dynamics: vertical component of rotated lateral mixing |
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| 23 | #else |
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| 24 | USE dynldf_iso,ONLY: akzu, akzv ! dynamics: vertical component of rotated lateral mixing |
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| 25 | #endif |
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| 26 | USE ldfdyn ! lateral diffusion: eddy viscosity coef. and type of operator |
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| 27 | USE trd_oce ! trends: ocean variables |
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| 28 | USE trddyn ! trend manager: dynamics |
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| 29 | ! |
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| 30 | USE in_out_manager ! I/O manager |
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| 31 | USE lib_mpp ! MPP library |
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| 32 | USE prtctl ! Print control |
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| 33 | USE timing ! Timing |
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| 34 | |
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| 35 | IMPLICIT NONE |
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| 36 | PRIVATE |
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| 37 | |
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| 38 | PUBLIC dyn_zdf ! routine called by step.F90 |
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| 39 | |
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| 40 | REAL(wp) :: r_vvl ! non-linear free surface indicator: =0 if ln_linssh=T, =1 otherwise |
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| 41 | |
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| 42 | !! * Substitutions |
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| 43 | # include "do_loop_substitute.h90" |
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| 44 | # include "domzgr_substitute.h90" |
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| 45 | !!---------------------------------------------------------------------- |
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| 46 | !! NEMO/OCE 4.0 , NEMO Consortium (2018) |
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| 47 | !! $Id$ |
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| 48 | !! Software governed by the CeCILL license (see ./LICENSE) |
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| 49 | !!---------------------------------------------------------------------- |
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| 50 | CONTAINS |
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| 51 | |
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| 52 | SUBROUTINE dyn_zdf( kt, Kbb, Kmm, Krhs, puu, pvv, Kaa ) |
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| 53 | !!---------------------------------------------------------------------- |
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| 54 | !! *** ROUTINE dyn_zdf *** |
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| 55 | !! |
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| 56 | !! ** Purpose : compute the trend due to the vert. momentum diffusion |
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| 57 | !! together with the Leap-Frog time stepping using an |
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| 58 | !! implicit scheme. |
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| 59 | !! |
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| 60 | !! ** Method : - Leap-Frog time stepping on all trends but the vertical mixing |
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| 61 | !! u(after) = u(before) + 2*dt * u(rhs) vector form or linear free surf. |
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| 62 | !! u(after) = ( e3u_b*u(before) + 2*dt * e3u_n*u(rhs) ) / e3u_after otherwise |
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| 63 | !! - update the after velocity with the implicit vertical mixing. |
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| 64 | !! This requires to solver the following system: |
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| 65 | !! u(after) = u(after) + 1/e3u_after dk+1[ mi(avm) / e3uw_after dk[ua] ] |
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| 66 | !! with the following surface/top/bottom boundary condition: |
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| 67 | !! surface: wind stress input (averaged over kt-1/2 & kt+1/2) |
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| 68 | !! top & bottom : top stress (iceshelf-ocean) & bottom stress (cf zdfdrg.F90) |
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| 69 | !! |
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| 70 | !! ** Action : (puu(:,:,:,Kaa),pvv(:,:,:,Kaa)) after velocity |
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| 71 | !!--------------------------------------------------------------------- |
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| 72 | INTEGER , INTENT( in ) :: kt ! ocean time-step index |
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| 73 | INTEGER , INTENT( in ) :: Kbb, Kmm, Krhs, Kaa ! ocean time level indices |
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| 74 | REAL(wp), DIMENSION(jpi,jpj,jpk,jpt), INTENT(inout) :: puu, pvv ! ocean velocities and RHS of momentum equation |
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| 75 | ! |
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| 76 | INTEGER :: ji, jj, jk ! dummy loop indices |
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| 77 | INTEGER :: iku, ikv ! local integers |
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| 78 | REAL(wp) :: zzwi, ze3ua, zdt ! local scalars |
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| 79 | REAL(wp) :: zzws, ze3va ! - - |
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| 80 | REAL(wp) :: z1_e3ua, z1_e3va ! - - |
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| 81 | REAL(wp) :: zWu , zWv ! - - |
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| 82 | REAL(wp) :: zWui, zWvi ! - - |
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| 83 | REAL(wp) :: zWus, zWvs ! - - |
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| 84 | REAL(wp), DIMENSION(A2D(nn_hls),jpk) :: zwi, zwd, zws ! 3D workspace |
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| 85 | REAL(wp), DIMENSION(:,:,:), ALLOCATABLE :: ztrdu, ztrdv ! - - |
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| 86 | !!--------------------------------------------------------------------- |
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| 87 | ! |
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| 88 | IF( ln_timing ) CALL timing_start('dyn_zdf') |
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| 89 | ! |
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| 90 | IF( .NOT. l_istiled .OR. ntile == 1 ) THEN ! Do only on the first tile |
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| 91 | IF( kt == nit000 ) THEN !* initialization |
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| 92 | IF(lwp) WRITE(numout,*) |
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| 93 | IF(lwp) WRITE(numout,*) 'dyn_zdf_imp : vertical momentum diffusion implicit operator' |
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| 94 | IF(lwp) WRITE(numout,*) '~~~~~~~~~~~ ' |
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| 95 | ! |
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| 96 | If( ln_linssh ) THEN ; r_vvl = 0._wp ! non-linear free surface indicator |
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| 97 | ELSE ; r_vvl = 1._wp |
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| 98 | ENDIF |
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| 99 | ENDIF |
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| 100 | ENDIF |
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| 101 | ! !* explicit top/bottom drag case |
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| 102 | IF( .NOT.ln_drgimp ) CALL zdf_drg_exp( kt, Kmm, puu(:,:,:,Kbb), pvv(:,:,:,Kbb), puu(:,:,:,Krhs), pvv(:,:,:,Krhs) ) ! add top/bottom friction trend to (puu(Kaa),pvv(Kaa)) |
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| 103 | ! |
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| 104 | ! |
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| 105 | IF( l_trddyn ) THEN !* temporary save of ta and sa trends |
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| 106 | ALLOCATE( ztrdu(jpi,jpj,jpk), ztrdv(jpi,jpj,jpk) ) |
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| 107 | ztrdu(:,:,:) = puu(:,:,:,Krhs) |
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| 108 | ztrdv(:,:,:) = pvv(:,:,:,Krhs) |
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| 109 | ENDIF |
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| 110 | ! |
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| 111 | ! !== RHS: Leap-Frog time stepping on all trends but the vertical mixing ==! (put in puu(:,:,:,Kaa),pvv(:,:,:,Kaa)) |
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| 112 | ! |
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| 113 | ! ! time stepping except vertical diffusion |
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| 114 | IF( ln_dynadv_vec .OR. ln_linssh ) THEN ! applied on velocity |
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| 115 | DO_3D( 0, 0, 0, 0, 1, jpkm1 ) |
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| 116 | puu(ji,jj,jk,Kaa) = ( puu(ji,jj,jk,Kbb) + rDt * puu(ji,jj,jk,Krhs) ) * umask(ji,jj,jk) |
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| 117 | pvv(ji,jj,jk,Kaa) = ( pvv(ji,jj,jk,Kbb) + rDt * pvv(ji,jj,jk,Krhs) ) * vmask(ji,jj,jk) |
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| 118 | END_3D |
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| 119 | ELSE ! applied on thickness weighted velocity |
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| 120 | DO_3D( 0, 0, 0, 0, 1, jpkm1 ) |
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| 121 | puu(ji,jj,jk,Kaa) = ( e3u(ji,jj,jk,Kbb) * puu(ji,jj,jk,Kbb ) & |
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| 122 | & + rDt * e3u(ji,jj,jk,Kmm) * puu(ji,jj,jk,Krhs) ) & |
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| 123 | & / e3u(ji,jj,jk,Kaa) * umask(ji,jj,jk) |
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| 124 | pvv(ji,jj,jk,Kaa) = ( e3v(ji,jj,jk,Kbb) * pvv(ji,jj,jk,Kbb ) & |
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| 125 | & + rDt * e3v(ji,jj,jk,Kmm) * pvv(ji,jj,jk,Krhs) ) & |
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| 126 | & / e3v(ji,jj,jk,Kaa) * vmask(ji,jj,jk) |
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| 127 | END_3D |
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| 128 | ENDIF |
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| 129 | ! ! add top/bottom friction |
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| 130 | ! With split-explicit free surface, barotropic stress is treated explicitly Update velocities at the bottom. |
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| 131 | ! J. Chanut: The bottom stress is computed considering after barotropic velocities, which does |
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| 132 | ! not lead to the effective stress seen over the whole barotropic loop. |
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| 133 | ! G. Madec : in linear free surface, e3u(:,:,:,Kaa) = e3u(:,:,:,Kmm) = e3u_0, so systematic use of e3u(:,:,:,Kaa) |
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| 134 | IF( ln_drgimp .AND. ln_dynspg_ts ) THEN |
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| 135 | DO_3D( 0, 0, 0, 0, 1, jpkm1 ) ! remove barotropic velocities |
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| 136 | puu(ji,jj,jk,Kaa) = ( puu(ji,jj,jk,Kaa) - uu_b(ji,jj,Kaa) ) * umask(ji,jj,jk) |
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| 137 | pvv(ji,jj,jk,Kaa) = ( pvv(ji,jj,jk,Kaa) - vv_b(ji,jj,Kaa) ) * vmask(ji,jj,jk) |
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| 138 | END_3D |
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| 139 | DO_2D( 0, 0, 0, 0 ) ! Add bottom/top stress due to barotropic component only |
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| 140 | iku = mbku(ji,jj) ! ocean bottom level at u- and v-points |
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| 141 | ikv = mbkv(ji,jj) ! (deepest ocean u- and v-points) |
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| 142 | ze3ua = ( 1._wp - r_vvl ) * e3u(ji,jj,iku,Kmm) & |
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| 143 | & + r_vvl * e3u(ji,jj,iku,Kaa) |
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| 144 | ze3va = ( 1._wp - r_vvl ) * e3v(ji,jj,ikv,Kmm) & |
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| 145 | & + r_vvl * e3v(ji,jj,ikv,Kaa) |
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| 146 | puu(ji,jj,iku,Kaa) = puu(ji,jj,iku,Kaa) + rDt * 0.5*( rCdU_bot(ji+1,jj)+rCdU_bot(ji,jj) ) * uu_b(ji,jj,Kaa) / ze3ua |
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| 147 | pvv(ji,jj,ikv,Kaa) = pvv(ji,jj,ikv,Kaa) + rDt * 0.5*( rCdU_bot(ji,jj+1)+rCdU_bot(ji,jj) ) * vv_b(ji,jj,Kaa) / ze3va |
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| 148 | END_2D |
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| 149 | IF( ln_isfcav.OR.ln_drgice_imp ) THEN ! Ocean cavities (ISF) |
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| 150 | DO_2D( 0, 0, 0, 0 ) |
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| 151 | iku = miku(ji,jj) ! top ocean level at u- and v-points |
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| 152 | ikv = mikv(ji,jj) ! (first wet ocean u- and v-points) |
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| 153 | ze3ua = ( 1._wp - r_vvl ) * e3u(ji,jj,iku,Kmm) & |
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| 154 | & + r_vvl * e3u(ji,jj,iku,Kaa) |
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| 155 | ze3va = ( 1._wp - r_vvl ) * e3v(ji,jj,ikv,Kmm) & |
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| 156 | & + r_vvl * e3v(ji,jj,ikv,Kaa) |
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| 157 | puu(ji,jj,iku,Kaa) = puu(ji,jj,iku,Kaa) + rDt * 0.5*( rCdU_top(ji+1,jj)+rCdU_top(ji,jj) ) * uu_b(ji,jj,Kaa) / ze3ua |
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| 158 | pvv(ji,jj,ikv,Kaa) = pvv(ji,jj,ikv,Kaa) + rDt * 0.5*( rCdU_top(ji,jj+1)+rCdU_top(ji,jj) ) * vv_b(ji,jj,Kaa) / ze3va |
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| 159 | END_2D |
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| 160 | END IF |
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| 161 | ENDIF |
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| 162 | ! |
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| 163 | ! !== Vertical diffusion on u ==! |
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| 164 | ! |
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| 165 | ! !* Matrix construction |
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| 166 | zdt = rDt * 0.5 |
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| 167 | IF( ln_zad_Aimp ) THEN !! |
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| 168 | SELECT CASE( nldf_dyn ) |
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| 169 | CASE( np_lap_i ) ! rotated lateral mixing: add its vertical mixing (akzu) |
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| 170 | DO_3D( 0, 0, 0, 0, 1, jpkm1 ) |
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| 171 | ze3ua = ( 1._wp - r_vvl ) * e3u(ji,jj,jk,Kmm) & |
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| 172 | & + r_vvl * e3u(ji,jj,jk,Kaa) ! after scale factor at U-point |
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| 173 | zzwi = - zdt * ( avm(ji+1,jj,jk ) + avm(ji,jj,jk ) + akzu(ji,jj,jk ) ) & |
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| 174 | & / ( ze3ua * e3uw(ji,jj,jk ,Kmm) ) * wumask(ji,jj,jk ) |
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| 175 | zzws = - zdt * ( avm(ji+1,jj,jk+1) + avm(ji,jj,jk+1) + akzu(ji,jj,jk+1) ) & |
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| 176 | & / ( ze3ua * e3uw(ji,jj,jk+1,Kmm) ) * wumask(ji,jj,jk+1) |
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| 177 | zWui = ( wi(ji,jj,jk ) + wi(ji+1,jj,jk ) ) / ze3ua |
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| 178 | zWus = ( wi(ji,jj,jk+1) + wi(ji+1,jj,jk+1) ) / ze3ua |
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| 179 | zwi(ji,jj,jk) = zzwi + zdt * MIN( zWui, 0._wp ) |
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| 180 | zws(ji,jj,jk) = zzws - zdt * MAX( zWus, 0._wp ) |
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| 181 | zwd(ji,jj,jk) = 1._wp - zzwi - zzws + zdt * ( MAX( zWui, 0._wp ) - MIN( zWus, 0._wp ) ) |
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| 182 | END_3D |
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| 183 | CASE DEFAULT ! iso-level lateral mixing |
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| 184 | DO_3D( 0, 0, 0, 0, 1, jpkm1 ) |
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| 185 | ze3ua = ( 1._wp - r_vvl ) * e3u(ji,jj,jk,Kmm) & ! after scale factor at U-point |
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| 186 | & + r_vvl * e3u(ji,jj,jk,Kaa) |
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| 187 | zzwi = - zdt * ( avm(ji+1,jj,jk ) + avm(ji,jj,jk ) ) & |
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| 188 | & / ( ze3ua * e3uw(ji,jj,jk ,Kmm) ) * wumask(ji,jj,jk ) |
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| 189 | zzws = - zdt * ( avm(ji+1,jj,jk+1) + avm(ji,jj,jk+1) ) & |
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| 190 | & / ( ze3ua * e3uw(ji,jj,jk+1,Kmm) ) * wumask(ji,jj,jk+1) |
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| 191 | zWui = ( wi(ji,jj,jk ) + wi(ji+1,jj,jk ) ) / ze3ua |
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| 192 | zWus = ( wi(ji,jj,jk+1) + wi(ji+1,jj,jk+1) ) / ze3ua |
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| 193 | zwi(ji,jj,jk) = zzwi + zdt * MIN( zWui, 0._wp ) |
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| 194 | zws(ji,jj,jk) = zzws - zdt * MAX( zWus, 0._wp ) |
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| 195 | zwd(ji,jj,jk) = 1._wp - zzwi - zzws + zdt * ( MAX( zWui, 0._wp ) - MIN( zWus, 0._wp ) ) |
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| 196 | END_3D |
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| 197 | END SELECT |
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| 198 | DO_2D( 0, 0, 0, 0 ) !* Surface boundary conditions |
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| 199 | zwi(ji,jj,1) = 0._wp |
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| 200 | ze3ua = ( 1._wp - r_vvl ) * e3u(ji,jj,1,Kmm) & |
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| 201 | & + r_vvl * e3u(ji,jj,1,Kaa) |
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| 202 | zzws = - zdt * ( avm(ji+1,jj,2) + avm(ji ,jj,2) ) & |
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| 203 | & / ( ze3ua * e3uw(ji,jj,2,Kmm) ) * wumask(ji,jj,2) |
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| 204 | zWus = ( wi(ji ,jj,2) + wi(ji+1,jj,2) ) / ze3ua |
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| 205 | zws(ji,jj,1 ) = zzws - zdt * MAX( zWus, 0._wp ) |
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| 206 | zwd(ji,jj,1 ) = 1._wp - zzws - zdt * ( MIN( zWus, 0._wp ) ) |
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| 207 | END_2D |
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| 208 | ELSE |
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| 209 | SELECT CASE( nldf_dyn ) |
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| 210 | CASE( np_lap_i ) ! rotated lateral mixing: add its vertical mixing (akzu) |
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| 211 | DO_3D( 0, 0, 0, 0, 1, jpkm1 ) |
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| 212 | ze3ua = ( 1._wp - r_vvl ) * e3u(ji,jj,jk,Kmm) & |
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| 213 | & + r_vvl * e3u(ji,jj,jk,Kaa) ! after scale factor at U-point |
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| 214 | zzwi = - zdt * ( avm(ji+1,jj,jk ) + avm(ji,jj,jk ) + akzu(ji,jj,jk ) ) & |
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| 215 | & / ( ze3ua * e3uw(ji,jj,jk ,Kmm) ) * wumask(ji,jj,jk ) |
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| 216 | zzws = - zdt * ( avm(ji+1,jj,jk+1) + avm(ji,jj,jk+1) + akzu(ji,jj,jk+1) ) & |
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| 217 | & / ( ze3ua * e3uw(ji,jj,jk+1,Kmm) ) * wumask(ji,jj,jk+1) |
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| 218 | zwi(ji,jj,jk) = zzwi |
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| 219 | zws(ji,jj,jk) = zzws |
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| 220 | zwd(ji,jj,jk) = 1._wp - zzwi - zzws |
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| 221 | END_3D |
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| 222 | CASE DEFAULT ! iso-level lateral mixing |
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| 223 | DO_3D( 0, 0, 0, 0, 1, jpkm1 ) |
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| 224 | ze3ua = ( 1._wp - r_vvl ) * e3u(ji,jj,jk,Kmm) & |
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| 225 | & + r_vvl * e3u(ji,jj,jk,Kaa) ! after scale factor at U-point |
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| 226 | zzwi = - zdt * ( avm(ji+1,jj,jk ) + avm(ji,jj,jk ) ) & |
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| 227 | & / ( ze3ua * e3uw(ji,jj,jk ,Kmm) ) * wumask(ji,jj,jk ) |
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| 228 | zzws = - zdt * ( avm(ji+1,jj,jk+1) + avm(ji,jj,jk+1) ) & |
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| 229 | & / ( ze3ua * e3uw(ji,jj,jk+1,Kmm) ) * wumask(ji,jj,jk+1) |
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| 230 | zwi(ji,jj,jk) = zzwi |
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| 231 | zws(ji,jj,jk) = zzws |
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| 232 | zwd(ji,jj,jk) = 1._wp - zzwi - zzws |
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| 233 | END_3D |
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| 234 | END SELECT |
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| 235 | DO_2D( 0, 0, 0, 0 ) !* Surface boundary conditions |
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| 236 | zwi(ji,jj,1) = 0._wp |
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| 237 | zwd(ji,jj,1) = 1._wp - zws(ji,jj,1) |
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| 238 | END_2D |
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| 239 | ENDIF |
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| 240 | ! |
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| 241 | ! |
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| 242 | ! !== Apply semi-implicit bottom friction ==! |
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| 243 | ! |
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| 244 | ! Only needed for semi-implicit bottom friction setup. The explicit |
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| 245 | ! bottom friction has been included in "u(v)a" which act as the R.H.S |
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| 246 | ! column vector of the tri-diagonal matrix equation |
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| 247 | ! |
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| 248 | IF ( ln_drgimp ) THEN ! implicit bottom friction |
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| 249 | DO_2D( 0, 0, 0, 0 ) |
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| 250 | iku = mbku(ji,jj) ! ocean bottom level at u- and v-points |
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| 251 | ze3ua = ( 1._wp - r_vvl ) * e3u(ji,jj,iku,Kmm) & |
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| 252 | & + r_vvl * e3u(ji,jj,iku,Kaa) ! after scale factor at T-point |
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| 253 | zwd(ji,jj,iku) = zwd(ji,jj,iku) - rDt * 0.5*( rCdU_bot(ji+1,jj)+rCdU_bot(ji,jj) ) / ze3ua |
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| 254 | END_2D |
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| 255 | IF ( ln_isfcav.OR.ln_drgice_imp ) THEN ! top friction (always implicit) |
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| 256 | DO_2D( 0, 0, 0, 0 ) |
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| 257 | !!gm top Cd is masked (=0 outside cavities) no need of test on mik>=2 ==>> it has been suppressed |
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| 258 | iku = miku(ji,jj) ! ocean top level at u- and v-points |
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| 259 | ze3ua = ( 1._wp - r_vvl ) * e3u(ji,jj,iku,Kmm) & |
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| 260 | & + r_vvl * e3u(ji,jj,iku,Kaa) ! after scale factor at T-point |
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| 261 | zwd(ji,jj,iku) = zwd(ji,jj,iku) - rDt * 0.5*( rCdU_top(ji+1,jj)+rCdU_top(ji,jj) ) / ze3ua |
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| 262 | END_2D |
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| 263 | END IF |
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| 264 | ENDIF |
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| 265 | ! |
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| 266 | ! Matrix inversion starting from the first level |
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| 267 | !----------------------------------------------------------------------- |
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| 268 | ! solve m.x = y where m is a tri diagonal matrix ( jpk*jpk ) |
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| 269 | ! |
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| 270 | ! ( zwd1 zws1 0 0 0 )( zwx1 ) ( zwy1 ) |
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| 271 | ! ( zwi2 zwd2 zws2 0 0 )( zwx2 ) ( zwy2 ) |
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| 272 | ! ( 0 zwi3 zwd3 zws3 0 )( zwx3 )=( zwy3 ) |
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| 273 | ! ( ... )( ... ) ( ... ) |
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| 274 | ! ( 0 0 0 zwik zwdk )( zwxk ) ( zwyk ) |
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| 275 | ! |
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| 276 | ! m is decomposed in the product of an upper and a lower triangular matrix |
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| 277 | ! The 3 diagonal terms are in 2d arrays: zwd, zws, zwi |
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| 278 | ! The solution (the after velocity) is in puu(:,:,:,Kaa) |
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| 279 | !----------------------------------------------------------------------- |
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| 280 | ! |
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| 281 | DO_3D( 0, 0, 0, 0, 2, jpkm1 ) !== First recurrence : Dk = Dk - Lk * Uk-1 / Dk-1 (increasing k) == |
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| 282 | 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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| 283 | END_3D |
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| 284 | ! |
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| 285 | DO_2D( 0, 0, 0, 0 ) !== second recurrence: SOLk = RHSk - Lk / Dk-1 Lk-1 ==! |
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| 286 | ze3ua = ( 1._wp - r_vvl ) * e3u(ji,jj,1,Kmm) & |
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| 287 | & + r_vvl * e3u(ji,jj,1,Kaa) |
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| 288 | puu(ji,jj,1,Kaa) = puu(ji,jj,1,Kaa) + rDt * 0.5_wp * ( utau_b(ji,jj) + utau(ji,jj) ) & |
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| 289 | & / ( ze3ua * rho0 ) * umask(ji,jj,1) |
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| 290 | END_2D |
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| 291 | DO_3D( 0, 0, 0, 0, 2, jpkm1 ) |
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| 292 | puu(ji,jj,jk,Kaa) = puu(ji,jj,jk,Kaa) - zwi(ji,jj,jk) / zwd(ji,jj,jk-1) * puu(ji,jj,jk-1,Kaa) |
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| 293 | END_3D |
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| 294 | ! |
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| 295 | DO_2D( 0, 0, 0, 0 ) !== thrid recurrence : SOLk = ( Lk - Uk * Ek+1 ) / Dk ==! |
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| 296 | puu(ji,jj,jpkm1,Kaa) = puu(ji,jj,jpkm1,Kaa) / zwd(ji,jj,jpkm1) |
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| 297 | END_2D |
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| 298 | DO_3DS( 0, 0, 0, 0, jpk-2, 1, -1 ) |
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| 299 | puu(ji,jj,jk,Kaa) = ( puu(ji,jj,jk,Kaa) - zws(ji,jj,jk) * puu(ji,jj,jk+1,Kaa) ) / zwd(ji,jj,jk) |
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| 300 | END_3D |
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| 301 | ! |
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| 302 | ! !== Vertical diffusion on v ==! |
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| 303 | ! |
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| 304 | ! !* Matrix construction |
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| 305 | zdt = rDt * 0.5 |
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| 306 | IF( ln_zad_Aimp ) THEN !! |
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| 307 | SELECT CASE( nldf_dyn ) |
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| 308 | CASE( np_lap_i ) ! rotated lateral mixing: add its vertical mixing (akzv) |
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| 309 | DO_3D( 0, 0, 0, 0, 1, jpkm1 ) |
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| 310 | ze3va = ( 1._wp - r_vvl ) * e3v(ji,jj,jk,Kmm) & |
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| 311 | & + r_vvl * e3v(ji,jj,jk,Kaa) ! after scale factor at V-point |
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| 312 | zzwi = - zdt * ( avm(ji,jj+1,jk ) + avm(ji,jj,jk ) + akzv(ji,jj,jk ) ) & |
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| 313 | & / ( ze3va * e3vw(ji,jj,jk ,Kmm) ) * wvmask(ji,jj,jk ) |
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| 314 | zzws = - zdt * ( avm(ji,jj+1,jk+1) + avm(ji,jj,jk+1) + akzv(ji,jj,jk+1) ) & |
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| 315 | & / ( ze3va * e3vw(ji,jj,jk+1,Kmm) ) * wvmask(ji,jj,jk+1) |
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| 316 | zWvi = ( wi(ji,jj,jk ) + wi(ji,jj+1,jk ) ) / ze3va |
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| 317 | zWvs = ( wi(ji,jj,jk+1) + wi(ji,jj+1,jk+1) ) / ze3va |
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| 318 | zwi(ji,jj,jk) = zzwi + zdt * MIN( zWvi, 0._wp ) |
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| 319 | zws(ji,jj,jk) = zzws - zdt * MAX( zWvs, 0._wp ) |
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| 320 | zwd(ji,jj,jk) = 1._wp - zzwi - zzws - zdt * ( - MAX( zWvi, 0._wp ) + MIN( zWvs, 0._wp ) ) |
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| 321 | END_3D |
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| 322 | CASE DEFAULT ! iso-level lateral mixing |
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| 323 | DO_3D( 0, 0, 0, 0, 1, jpkm1 ) |
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| 324 | ze3va = ( 1._wp - r_vvl ) * e3v(ji,jj,jk,Kmm) & |
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| 325 | & + r_vvl * e3v(ji,jj,jk,Kaa) ! after scale factor at V-point |
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| 326 | zzwi = - zdt * ( avm(ji,jj+1,jk ) + avm(ji,jj,jk ) ) & |
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| 327 | & / ( ze3va * e3vw(ji,jj,jk ,Kmm) ) * wvmask(ji,jj,jk ) |
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| 328 | zzws = - zdt * ( avm(ji,jj+1,jk+1) + avm(ji,jj,jk+1) ) & |
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| 329 | & / ( ze3va * e3vw(ji,jj,jk+1,Kmm) ) * wvmask(ji,jj,jk+1) |
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| 330 | zWvi = ( wi(ji,jj,jk ) + wi(ji,jj+1,jk ) ) / ze3va |
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| 331 | zWvs = ( wi(ji,jj,jk+1) + wi(ji,jj+1,jk+1) ) / ze3va |
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| 332 | zwi(ji,jj,jk) = zzwi + zdt * MIN( zWvi, 0._wp ) |
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| 333 | zws(ji,jj,jk) = zzws - zdt * MAX( zWvs, 0._wp ) |
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| 334 | zwd(ji,jj,jk) = 1._wp - zzwi - zzws - zdt * ( - MAX( zWvi, 0._wp ) + MIN( zWvs, 0._wp ) ) |
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| 335 | END_3D |
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| 336 | END SELECT |
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| 337 | DO_2D( 0, 0, 0, 0 ) !* Surface boundary conditions |
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| 338 | zwi(ji,jj,1) = 0._wp |
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| 339 | ze3va = ( 1._wp - r_vvl ) * e3v(ji,jj,1,Kmm) & |
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| 340 | & + r_vvl * e3v(ji,jj,1,Kaa) |
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| 341 | zzws = - zdt * ( avm(ji,jj+1,2) + avm(ji,jj,2) ) & |
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| 342 | & / ( ze3va * e3vw(ji,jj,2,Kmm) ) * wvmask(ji,jj,2) |
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| 343 | zWvs = ( wi(ji,jj ,2) + wi(ji,jj+1,2) ) / ze3va |
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| 344 | zws(ji,jj,1 ) = zzws - zdt * MAX( zWvs, 0._wp ) |
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| 345 | zwd(ji,jj,1 ) = 1._wp - zzws - zdt * ( MIN( zWvs, 0._wp ) ) |
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| 346 | END_2D |
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| 347 | ELSE |
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| 348 | SELECT CASE( nldf_dyn ) |
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| 349 | CASE( np_lap_i ) ! rotated lateral mixing: add its vertical mixing (akzu) |
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| 350 | DO_3D( 0, 0, 0, 0, 1, jpkm1 ) |
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| 351 | ze3va = ( 1._wp - r_vvl ) * e3v(ji,jj,jk,Kmm) & |
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| 352 | & + r_vvl * e3v(ji,jj,jk,Kaa) ! after scale factor at V-point |
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| 353 | zzwi = - zdt * ( avm(ji,jj+1,jk ) + avm(ji,jj,jk ) + akzv(ji,jj,jk ) ) & |
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| 354 | & / ( ze3va * e3vw(ji,jj,jk ,Kmm) ) * wvmask(ji,jj,jk ) |
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| 355 | zzws = - zdt * ( avm(ji,jj+1,jk+1) + avm(ji,jj,jk+1) + akzv(ji,jj,jk+1) ) & |
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| 356 | & / ( ze3va * e3vw(ji,jj,jk+1,Kmm) ) * wvmask(ji,jj,jk+1) |
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| 357 | zwi(ji,jj,jk) = zzwi |
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| 358 | zws(ji,jj,jk) = zzws |
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| 359 | zwd(ji,jj,jk) = 1._wp - zzwi - zzws |
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| 360 | END_3D |
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| 361 | CASE DEFAULT ! iso-level lateral mixing |
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| 362 | DO_3D( 0, 0, 0, 0, 1, jpkm1 ) |
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| 363 | ze3va = ( 1._wp - r_vvl ) * e3v(ji,jj,jk,Kmm) & |
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| 364 | & + r_vvl * e3v(ji,jj,jk,Kaa) ! after scale factor at V-point |
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| 365 | zzwi = - zdt * ( avm(ji,jj+1,jk ) + avm(ji,jj,jk ) ) & |
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| 366 | & / ( ze3va * e3vw(ji,jj,jk ,Kmm) ) * wvmask(ji,jj,jk ) |
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| 367 | zzws = - zdt * ( avm(ji,jj+1,jk+1) + avm(ji,jj,jk+1) ) & |
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| 368 | & / ( ze3va * e3vw(ji,jj,jk+1,Kmm) ) * wvmask(ji,jj,jk+1) |
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| 369 | zwi(ji,jj,jk) = zzwi |
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| 370 | zws(ji,jj,jk) = zzws |
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| 371 | zwd(ji,jj,jk) = 1._wp - zzwi - zzws |
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| 372 | END_3D |
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| 373 | END SELECT |
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| 374 | DO_2D( 0, 0, 0, 0 ) !* Surface boundary conditions |
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| 375 | zwi(ji,jj,1) = 0._wp |
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| 376 | zwd(ji,jj,1) = 1._wp - zws(ji,jj,1) |
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| 377 | END_2D |
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| 378 | ENDIF |
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| 379 | ! |
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| 380 | ! !== Apply semi-implicit top/bottom friction ==! |
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| 381 | ! |
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| 382 | ! Only needed for semi-implicit bottom friction setup. The explicit |
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| 383 | ! bottom friction has been included in "u(v)a" which act as the R.H.S |
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| 384 | ! column vector of the tri-diagonal matrix equation |
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| 385 | ! |
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| 386 | IF( ln_drgimp ) THEN |
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| 387 | DO_2D( 0, 0, 0, 0 ) |
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| 388 | ikv = mbkv(ji,jj) ! (deepest ocean u- and v-points) |
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| 389 | ze3va = ( 1._wp - r_vvl ) * e3v(ji,jj,ikv,Kmm) & |
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| 390 | & + r_vvl * e3v(ji,jj,ikv,Kaa) ! after scale factor at T-point |
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| 391 | zwd(ji,jj,ikv) = zwd(ji,jj,ikv) - rDt * 0.5*( rCdU_bot(ji,jj+1)+rCdU_bot(ji,jj) ) / ze3va |
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| 392 | END_2D |
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| 393 | IF ( ln_isfcav.OR.ln_drgice_imp ) THEN |
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| 394 | DO_2D( 0, 0, 0, 0 ) |
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| 395 | ikv = mikv(ji,jj) ! (first wet ocean u- and v-points) |
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| 396 | ze3va = ( 1._wp - r_vvl ) * e3v(ji,jj,ikv,Kmm) & |
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| 397 | & + r_vvl * e3v(ji,jj,ikv,Kaa) ! after scale factor at T-point |
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| 398 | zwd(ji,jj,ikv) = zwd(ji,jj,ikv) - rDt * 0.5*( rCdU_top(ji,jj+1)+rCdU_top(ji,jj) ) / ze3va |
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| 399 | END_2D |
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| 400 | ENDIF |
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| 401 | ENDIF |
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| 402 | |
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| 403 | ! Matrix inversion |
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| 404 | !----------------------------------------------------------------------- |
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| 405 | ! solve m.x = y where m is a tri diagonal matrix ( jpk*jpk ) |
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| 406 | ! |
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| 407 | ! ( zwd1 zws1 0 0 0 )( zwx1 ) ( zwy1 ) |
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| 408 | ! ( zwi2 zwd2 zws2 0 0 )( zwx2 ) ( zwy2 ) |
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| 409 | ! ( 0 zwi3 zwd3 zws3 0 )( zwx3 )=( zwy3 ) |
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| 410 | ! ( ... )( ... ) ( ... ) |
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| 411 | ! ( 0 0 0 zwik zwdk )( zwxk ) ( zwyk ) |
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| 412 | ! |
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| 413 | ! m is decomposed in the product of an upper and lower triangular matrix |
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| 414 | ! The 3 diagonal terms are in 2d arrays: zwd, zws, zwi |
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| 415 | ! The solution (after velocity) is in 2d array va |
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| 416 | !----------------------------------------------------------------------- |
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| 417 | ! |
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| 418 | DO_3D( 0, 0, 0, 0, 2, jpkm1 ) !== First recurrence : Dk = Dk - Lk * Uk-1 / Dk-1 (increasing k) == |
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| 419 | 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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| 420 | END_3D |
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| 421 | ! |
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| 422 | DO_2D( 0, 0, 0, 0 ) !== second recurrence: SOLk = RHSk - Lk / Dk-1 Lk-1 ==! |
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| 423 | ze3va = ( 1._wp - r_vvl ) * e3v(ji,jj,1,Kmm) & |
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| 424 | & + r_vvl * e3v(ji,jj,1,Kaa) |
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| 425 | pvv(ji,jj,1,Kaa) = pvv(ji,jj,1,Kaa) + rDt * 0.5_wp * ( vtau_b(ji,jj) + vtau(ji,jj) ) & |
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| 426 | & / ( ze3va * rho0 ) * vmask(ji,jj,1) |
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| 427 | END_2D |
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| 428 | DO_3D( 0, 0, 0, 0, 2, jpkm1 ) |
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| 429 | pvv(ji,jj,jk,Kaa) = pvv(ji,jj,jk,Kaa) - zwi(ji,jj,jk) / zwd(ji,jj,jk-1) * pvv(ji,jj,jk-1,Kaa) |
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| 430 | END_3D |
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| 431 | ! |
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| 432 | DO_2D( 0, 0, 0, 0 ) !== third recurrence : SOLk = ( Lk - Uk * SOLk+1 ) / Dk ==! |
|---|
| 433 | pvv(ji,jj,jpkm1,Kaa) = pvv(ji,jj,jpkm1,Kaa) / zwd(ji,jj,jpkm1) |
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| 434 | END_2D |
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| 435 | DO_3DS( 0, 0, 0, 0, jpk-2, 1, -1 ) |
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| 436 | pvv(ji,jj,jk,Kaa) = ( pvv(ji,jj,jk,Kaa) - zws(ji,jj,jk) * pvv(ji,jj,jk+1,Kaa) ) / zwd(ji,jj,jk) |
|---|
| 437 | END_3D |
|---|
| 438 | ! |
|---|
| 439 | IF( l_trddyn ) THEN ! save the vertical diffusive trends for further diagnostics |
|---|
| 440 | ztrdu(:,:,:) = ( puu(:,:,:,Kaa) - puu(:,:,:,Kbb) ) / rDt - ztrdu(:,:,:) |
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| 441 | ztrdv(:,:,:) = ( pvv(:,:,:,Kaa) - pvv(:,:,:,Kbb) ) / rDt - ztrdv(:,:,:) |
|---|
| 442 | CALL trd_dyn( ztrdu, ztrdv, jpdyn_zdf, kt, Kmm ) |
|---|
| 443 | DEALLOCATE( ztrdu, ztrdv ) |
|---|
| 444 | ENDIF |
|---|
| 445 | ! ! print mean trends (used for debugging) |
|---|
| 446 | IF(sn_cfctl%l_prtctl) CALL prt_ctl( tab3d_1=puu(:,:,:,Kaa), clinfo1=' zdf - Ua: ', mask1=umask, & |
|---|
| 447 | & tab3d_2=pvv(:,:,:,Kaa), clinfo2= ' Va: ', mask2=vmask, clinfo3='dyn' ) |
|---|
| 448 | ! |
|---|
| 449 | IF( ln_timing ) CALL timing_stop('dyn_zdf') |
|---|
| 450 | ! |
|---|
| 451 | END SUBROUTINE dyn_zdf |
|---|
| 452 | |
|---|
| 453 | !!============================================================================== |
|---|
| 454 | END MODULE dynzdf |
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