[643] | 1 | MODULE dynadv_ubs |
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| 2 | !!====================================================================== |
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| 3 | !! *** MODULE dynadv_ubs *** |
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| 4 | !! Ocean dynamics: Update the momentum trend with the flux form advection |
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| 5 | !! trend using a 3rd order upstream biased scheme |
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| 6 | !!====================================================================== |
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[1566] | 7 | !! History : 2.0 ! 2006-08 (R. Benshila, L. Debreu) Original code |
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| 8 | !! 3.2 ! 2009-07 (R. Benshila) Suppression of rigid-lid option |
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[643] | 9 | !!---------------------------------------------------------------------- |
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| 10 | |
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| 11 | !!---------------------------------------------------------------------- |
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| 12 | !! dyn_adv_ubs : flux form momentum advection using (ln_dynadv=T) |
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| 13 | !! an 3rd order Upstream Biased Scheme or Quick scheme |
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| 14 | !! combined with 2nd or 4th order finite differences |
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| 15 | !!---------------------------------------------------------------------- |
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| 16 | USE oce ! ocean dynamics and tracers |
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| 17 | USE dom_oce ! ocean space and time domain |
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[5062] | 18 | USE trd_oce ! trends: ocean variables |
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| 19 | USE trddyn ! trend manager: dynamics |
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| 20 | ! |
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[2715] | 21 | USE in_out_manager ! I/O manager |
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[1129] | 22 | USE prtctl ! Print control |
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[2715] | 23 | USE lbclnk ! ocean lateral boundary conditions (or mpp link) |
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| 24 | USE lib_mpp ! MPP library |
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[643] | 25 | |
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| 26 | IMPLICIT NONE |
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| 27 | PRIVATE |
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| 28 | |
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[3294] | 29 | REAL(wp), PARAMETER :: gamma1 = 1._wp/3._wp ! =1/4 quick ; =1/3 3rd order UBS |
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[4153] | 30 | REAL(wp), PARAMETER :: gamma2 = 1._wp/32._wp ! =0 2nd order ; =1/32 4th order centred |
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[643] | 31 | |
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[1566] | 32 | PUBLIC dyn_adv_ubs ! routine called by step.F90 |
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[643] | 33 | |
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| 34 | !! * Substitutions |
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| 35 | # include "vectopt_loop_substitute.h90" |
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| 36 | !!---------------------------------------------------------------------- |
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[9598] | 37 | !! NEMO/OCE 4.0 , NEMO Consortium (2018) |
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[1152] | 38 | !! $Id$ |
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[10068] | 39 | !! Software governed by the CeCILL license (see ./LICENSE) |
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[643] | 40 | !!---------------------------------------------------------------------- |
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| 41 | CONTAINS |
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| 42 | |
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| 43 | SUBROUTINE dyn_adv_ubs( kt ) |
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| 44 | !!---------------------------------------------------------------------- |
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| 45 | !! *** ROUTINE dyn_adv_ubs *** |
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| 46 | !! |
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| 47 | !! ** Purpose : Compute the now momentum advection trend in flux form |
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[1566] | 48 | !! and the general trend of the momentum equation. |
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[643] | 49 | !! |
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| 50 | !! ** Method : The scheme is the one implemeted in ROMS. It depends |
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| 51 | !! on two parameter gamma1 and gamma2. The former control the |
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| 52 | !! upstream baised part of the scheme and the later the centred |
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| 53 | !! part: gamma1 = 0 pure centered (no diffusive part) |
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| 54 | !! = 1/4 Quick scheme |
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| 55 | !! = 1/3 3rd order Upstream biased scheme |
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| 56 | !! gamma2 = 0 2nd order finite differencing |
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[4153] | 57 | !! = 1/32 4th order finite differencing |
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[643] | 58 | !! For stability reasons, the first term of the fluxes which cor- |
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| 59 | !! responds to a second order centered scheme is evaluated using |
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| 60 | !! the now velocity (centered in time) while the second term which |
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| 61 | !! is the diffusive part of the scheme, is evaluated using the |
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| 62 | !! before velocity (forward in time). |
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| 63 | !! Default value (hard coded in the begining of the module) are |
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[4153] | 64 | !! gamma1=1/3 and gamma2=1/32. |
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[643] | 65 | !! |
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[1566] | 66 | !! ** Action : - (ua,va) updated with the 3D advective momentum trends |
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[643] | 67 | !! |
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| 68 | !! Reference : Shchepetkin & McWilliams, 2005, Ocean Modelling. |
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| 69 | !!---------------------------------------------------------------------- |
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[6140] | 70 | INTEGER, INTENT(in) :: kt ! ocean time-step index |
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[2715] | 71 | ! |
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[6140] | 72 | INTEGER :: ji, jj, jk ! dummy loop indices |
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| 73 | REAL(wp) :: zui, zvj, zfuj, zfvi, zl_u, zl_v ! local scalars |
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[9019] | 74 | REAL(wp), DIMENSION(jpi,jpj,jpk) :: zfu_t, zfu_f, zfu_uw, zfu |
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| 75 | REAL(wp), DIMENSION(jpi,jpj,jpk) :: zfv_t, zfv_f, zfv_vw, zfv, zfw |
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| 76 | REAL(wp), DIMENSION(jpi,jpj,jpk,2) :: zlu_uu, zlu_uv |
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| 77 | REAL(wp), DIMENSION(jpi,jpj,jpk,2) :: zlv_vv, zlv_vu |
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[643] | 78 | !!---------------------------------------------------------------------- |
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[3294] | 79 | ! |
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[643] | 80 | IF( kt == nit000 ) THEN |
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| 81 | IF(lwp) WRITE(numout,*) |
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| 82 | IF(lwp) WRITE(numout,*) 'dyn_adv_ubs : UBS flux form momentum advection' |
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| 83 | IF(lwp) WRITE(numout,*) '~~~~~~~~~~~' |
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| 84 | ENDIF |
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[3294] | 85 | ! |
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[2715] | 86 | zfu_t(:,:,:) = 0._wp |
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| 87 | zfv_t(:,:,:) = 0._wp |
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| 88 | zfu_f(:,:,:) = 0._wp |
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| 89 | zfv_f(:,:,:) = 0._wp |
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[1566] | 90 | ! |
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[2715] | 91 | zlu_uu(:,:,:,:) = 0._wp |
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| 92 | zlv_vv(:,:,:,:) = 0._wp |
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| 93 | zlu_uv(:,:,:,:) = 0._wp |
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| 94 | zlv_vu(:,:,:,:) = 0._wp |
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[6140] | 95 | ! |
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| 96 | IF( l_trddyn ) THEN ! trends: store the input trends |
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[1129] | 97 | zfu_uw(:,:,:) = ua(:,:,:) |
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| 98 | zfv_vw(:,:,:) = va(:,:,:) |
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| 99 | ENDIF |
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[1566] | 100 | ! ! =========================== ! |
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| 101 | DO jk = 1, jpkm1 ! Laplacian of the velocity ! |
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| 102 | ! ! =========================== ! |
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| 103 | ! ! horizontal volume fluxes |
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[6140] | 104 | zfu(:,:,jk) = e2u(:,:) * e3u_n(:,:,jk) * un(:,:,jk) |
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| 105 | zfv(:,:,jk) = e1v(:,:) * e3v_n(:,:,jk) * vn(:,:,jk) |
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[1566] | 106 | ! |
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| 107 | DO jj = 2, jpjm1 ! laplacian |
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[643] | 108 | DO ji = fs_2, fs_jpim1 ! vector opt. |
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[5069] | 109 | zlu_uu(ji,jj,jk,1) = ( ub (ji+1,jj ,jk) - 2.*ub (ji,jj,jk) + ub (ji-1,jj ,jk) ) * umask(ji,jj,jk) |
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| 110 | zlv_vv(ji,jj,jk,1) = ( vb (ji ,jj+1,jk) - 2.*vb (ji,jj,jk) + vb (ji ,jj-1,jk) ) * vmask(ji,jj,jk) |
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| 111 | zlu_uv(ji,jj,jk,1) = ( ub (ji ,jj+1,jk) - ub (ji ,jj ,jk) ) * fmask(ji ,jj ,jk) & |
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| 112 | & - ( ub (ji ,jj ,jk) - ub (ji ,jj-1,jk) ) * fmask(ji ,jj-1,jk) |
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| 113 | zlv_vu(ji,jj,jk,1) = ( vb (ji+1,jj ,jk) - vb (ji ,jj ,jk) ) * fmask(ji ,jj ,jk) & |
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| 114 | & - ( vb (ji ,jj ,jk) - vb (ji-1,jj ,jk) ) * fmask(ji-1,jj ,jk) |
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[2715] | 115 | ! |
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[5069] | 116 | zlu_uu(ji,jj,jk,2) = ( zfu(ji+1,jj ,jk) - 2.*zfu(ji,jj,jk) + zfu(ji-1,jj ,jk) ) * umask(ji,jj,jk) |
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| 117 | zlv_vv(ji,jj,jk,2) = ( zfv(ji ,jj+1,jk) - 2.*zfv(ji,jj,jk) + zfv(ji ,jj-1,jk) ) * vmask(ji,jj,jk) |
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| 118 | zlu_uv(ji,jj,jk,2) = ( zfu(ji ,jj+1,jk) - zfu(ji ,jj ,jk) ) * fmask(ji ,jj ,jk) & |
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| 119 | & - ( zfu(ji ,jj ,jk) - zfu(ji ,jj-1,jk) ) * fmask(ji ,jj-1,jk) |
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| 120 | zlv_vu(ji,jj,jk,2) = ( zfv(ji+1,jj ,jk) - zfv(ji ,jj ,jk) ) * fmask(ji ,jj ,jk) & |
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| 121 | & - ( zfv(ji ,jj ,jk) - zfv(ji-1,jj ,jk) ) * fmask(ji-1,jj ,jk) |
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[643] | 122 | END DO |
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| 123 | END DO |
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[1566] | 124 | END DO |
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[10425] | 125 | CALL lbc_lnk_multi( 'dynadv_ubs', zlu_uu(:,:,:,1), 'U', 1. , zlu_uv(:,:,:,1), 'U', 1., & |
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[9090] | 126 | & zlu_uu(:,:,:,2), 'U', 1. , zlu_uv(:,:,:,2), 'U', 1., & |
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| 127 | & zlv_vv(:,:,:,1), 'V', 1. , zlv_vu(:,:,:,1), 'V', 1., & |
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| 128 | & zlv_vv(:,:,:,2), 'V', 1. , zlv_vu(:,:,:,2), 'V', 1. ) |
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[6140] | 129 | ! |
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[1566] | 130 | ! ! ====================== ! |
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| 131 | ! ! Horizontal advection ! |
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| 132 | DO jk = 1, jpkm1 ! ====================== ! |
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| 133 | ! ! horizontal volume fluxes |
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[6140] | 134 | zfu(:,:,jk) = 0.25_wp * e2u(:,:) * e3u_n(:,:,jk) * un(:,:,jk) |
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| 135 | zfv(:,:,jk) = 0.25_wp * e1v(:,:) * e3v_n(:,:,jk) * vn(:,:,jk) |
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[1566] | 136 | ! |
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| 137 | DO jj = 1, jpjm1 ! horizontal momentum fluxes at T- and F-point |
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[643] | 138 | DO ji = 1, fs_jpim1 ! vector opt. |
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| 139 | zui = ( un(ji,jj,jk) + un(ji+1,jj ,jk) ) |
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| 140 | zvj = ( vn(ji,jj,jk) + vn(ji ,jj+1,jk) ) |
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[1566] | 141 | ! |
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[6140] | 142 | IF( zui > 0 ) THEN ; zl_u = zlu_uu(ji ,jj,jk,1) |
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| 143 | ELSE ; zl_u = zlu_uu(ji+1,jj,jk,1) |
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[643] | 144 | ENDIF |
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[6140] | 145 | IF( zvj > 0 ) THEN ; zl_v = zlv_vv(ji,jj ,jk,1) |
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| 146 | ELSE ; zl_v = zlv_vv(ji,jj+1,jk,1) |
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[643] | 147 | ENDIF |
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[1566] | 148 | ! |
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[643] | 149 | zfu_t(ji+1,jj ,jk) = ( zfu(ji,jj,jk) + zfu(ji+1,jj ,jk) & |
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| 150 | & - gamma2 * ( zlu_uu(ji,jj,jk,2) + zlu_uu(ji+1,jj ,jk,2) ) ) & |
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| 151 | & * ( zui - gamma1 * zl_u) |
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| 152 | zfv_t(ji ,jj+1,jk) = ( zfv(ji,jj,jk) + zfv(ji ,jj+1,jk) & |
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| 153 | & - gamma2 * ( zlv_vv(ji,jj,jk,2) + zlv_vv(ji ,jj+1,jk,2) ) ) & |
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| 154 | & * ( zvj - gamma1 * zl_v) |
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[1566] | 155 | ! |
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[643] | 156 | zfuj = ( zfu(ji,jj,jk) + zfu(ji ,jj+1,jk) ) |
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| 157 | zfvi = ( zfv(ji,jj,jk) + zfv(ji+1,jj ,jk) ) |
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[6140] | 158 | IF( zfuj > 0 ) THEN ; zl_v = zlv_vu( ji ,jj ,jk,1) |
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| 159 | ELSE ; zl_v = zlv_vu( ji+1,jj,jk,1) |
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[643] | 160 | ENDIF |
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[6140] | 161 | IF( zfvi > 0 ) THEN ; zl_u = zlu_uv( ji,jj ,jk,1) |
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| 162 | ELSE ; zl_u = zlu_uv( ji,jj+1,jk,1) |
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[643] | 163 | ENDIF |
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[1566] | 164 | ! |
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[643] | 165 | zfv_f(ji ,jj ,jk) = ( zfvi - gamma2 * ( zlv_vu(ji,jj,jk,2) + zlv_vu(ji+1,jj ,jk,2) ) ) & |
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| 166 | & * ( un(ji,jj,jk) + un(ji ,jj+1,jk) - gamma1 * zl_u ) |
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| 167 | zfu_f(ji ,jj ,jk) = ( zfuj - gamma2 * ( zlu_uv(ji,jj,jk,2) + zlu_uv(ji ,jj+1,jk,2) ) ) & |
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| 168 | & * ( vn(ji,jj,jk) + vn(ji+1,jj ,jk) - gamma1 * zl_v ) |
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| 169 | END DO |
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| 170 | END DO |
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[1566] | 171 | DO jj = 2, jpjm1 ! divergence of horizontal momentum fluxes |
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[643] | 172 | DO ji = fs_2, fs_jpim1 ! vector opt. |
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[6140] | 173 | ua(ji,jj,jk) = ua(ji,jj,jk) - ( zfu_t(ji+1,jj,jk) - zfu_t(ji,jj ,jk) & |
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| 174 | & + zfv_f(ji ,jj,jk) - zfv_f(ji,jj-1,jk) ) * r1_e1e2u(ji,jj) / e3u_n(ji,jj,jk) |
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| 175 | va(ji,jj,jk) = va(ji,jj,jk) - ( zfu_f(ji,jj ,jk) - zfu_f(ji-1,jj,jk) & |
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| 176 | & + zfv_t(ji,jj+1,jk) - zfv_t(ji ,jj,jk) ) * r1_e1e2v(ji,jj) / e3v_n(ji,jj,jk) |
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[643] | 177 | END DO |
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| 178 | END DO |
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[1566] | 179 | END DO |
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[6140] | 180 | IF( l_trddyn ) THEN ! trends: send trends to trddyn for diagnostic |
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[1129] | 181 | zfu_uw(:,:,:) = ua(:,:,:) - zfu_uw(:,:,:) |
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| 182 | zfv_vw(:,:,:) = va(:,:,:) - zfv_vw(:,:,:) |
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[5062] | 183 | CALL trd_dyn( zfu_uw, zfv_vw, jpdyn_keg, kt ) |
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[1129] | 184 | zfu_t(:,:,:) = ua(:,:,:) |
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| 185 | zfv_t(:,:,:) = va(:,:,:) |
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| 186 | ENDIF |
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[1566] | 187 | ! ! ==================== ! |
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| 188 | ! ! Vertical advection ! |
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[6140] | 189 | ! ! ==================== ! |
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| 190 | DO jj = 2, jpjm1 ! surface/bottom advective fluxes set to zero |
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| 191 | DO ji = fs_2, fs_jpim1 |
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| 192 | zfu_uw(ji,jj,jpk) = 0._wp |
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| 193 | zfv_vw(ji,jj,jpk) = 0._wp |
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| 194 | zfu_uw(ji,jj, 1 ) = 0._wp |
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| 195 | zfv_vw(ji,jj, 1 ) = 0._wp |
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| 196 | END DO |
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| 197 | END DO |
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| 198 | IF( ln_linssh ) THEN ! constant volume : advection through the surface |
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| 199 | DO jj = 2, jpjm1 |
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| 200 | DO ji = fs_2, fs_jpim1 |
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| 201 | zfu_uw(ji,jj,1) = 0.5_wp * ( e1e2t(ji,jj) * wn(ji,jj,1) + e1e2t(ji+1,jj) * wn(ji+1,jj,1) ) * un(ji,jj,1) |
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| 202 | zfv_vw(ji,jj,1) = 0.5_wp * ( e1e2t(ji,jj) * wn(ji,jj,1) + e1e2t(ji,jj+1) * wn(ji,jj+1,1) ) * vn(ji,jj,1) |
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[643] | 203 | END DO |
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[6140] | 204 | END DO |
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| 205 | ENDIF |
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| 206 | DO jk = 2, jpkm1 ! interior fluxes |
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[6750] | 207 | DO jj = 2, jpj |
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| 208 | DO ji = 2, jpi |
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[6140] | 209 | zfw(ji,jj,jk) = 0.25_wp * e1e2t(ji,jj) * wn(ji,jj,jk) |
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| 210 | END DO |
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| 211 | END DO |
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| 212 | DO jj = 2, jpjm1 |
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| 213 | DO ji = fs_2, fs_jpim1 ! vector opt. |
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| 214 | zfu_uw(ji,jj,jk) = ( zfw(ji,jj,jk)+ zfw(ji+1,jj,jk) ) * ( un(ji,jj,jk) + un(ji,jj,jk-1) ) |
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| 215 | zfv_vw(ji,jj,jk) = ( zfw(ji,jj,jk)+ zfw(ji,jj+1,jk) ) * ( vn(ji,jj,jk) + vn(ji,jj,jk-1) ) |
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| 216 | END DO |
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| 217 | END DO |
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[643] | 218 | END DO |
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[6140] | 219 | DO jk = 1, jpkm1 ! divergence of vertical momentum flux divergence |
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| 220 | DO jj = 2, jpjm1 |
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[643] | 221 | DO ji = fs_2, fs_jpim1 ! vector opt. |
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[6140] | 222 | ua(ji,jj,jk) = ua(ji,jj,jk) - ( zfu_uw(ji,jj,jk) - zfu_uw(ji,jj,jk+1) ) * r1_e1e2u(ji,jj) / e3u_n(ji,jj,jk) |
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| 223 | va(ji,jj,jk) = va(ji,jj,jk) - ( zfv_vw(ji,jj,jk) - zfv_vw(ji,jj,jk+1) ) * r1_e1e2v(ji,jj) / e3v_n(ji,jj,jk) |
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[643] | 224 | END DO |
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| 225 | END DO |
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| 226 | END DO |
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[1566] | 227 | ! |
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[6140] | 228 | IF( l_trddyn ) THEN ! save the vertical advection trend for diagnostic |
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[1129] | 229 | zfu_t(:,:,:) = ua(:,:,:) - zfu_t(:,:,:) |
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| 230 | zfv_t(:,:,:) = va(:,:,:) - zfv_t(:,:,:) |
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[5062] | 231 | CALL trd_dyn( zfu_t, zfv_t, jpdyn_zad, kt ) |
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[1129] | 232 | ENDIF |
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[6140] | 233 | ! ! Control print |
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[1129] | 234 | IF(ln_ctl) CALL prt_ctl( tab3d_1=ua, clinfo1=' ubs2 adv - Ua: ', mask1=umask, & |
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| 235 | & tab3d_2=va, clinfo2= ' Va: ', mask2=vmask, clinfo3='dyn' ) |
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[1566] | 236 | ! |
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[643] | 237 | END SUBROUTINE dyn_adv_ubs |
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| 238 | |
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| 239 | !!============================================================================== |
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| 240 | END MODULE dynadv_ubs |
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