[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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| 18 | USE in_out_manager ! I/O manager |
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| 19 | USE lbclnk ! ocean lateral boundary conditions (or mpp link) |
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[1129] | 20 | USE trdmod ! ocean dynamics trends |
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| 21 | USE trdmod_oce ! ocean variables trends |
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| 22 | USE prtctl ! Print control |
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[643] | 23 | |
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| 24 | IMPLICIT NONE |
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| 25 | PRIVATE |
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| 26 | |
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| 27 | REAL(wp), PARAMETER :: gamma1 = 1._wp/4._wp ! =1/4 quick ; =1/3 3rd order UBS |
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| 28 | REAL(wp), PARAMETER :: gamma2 = 1._wp/8._wp ! =0 2nd order ; =1/8 4th order centred |
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| 29 | |
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[1566] | 30 | PUBLIC dyn_adv_ubs ! routine called by step.F90 |
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[643] | 31 | |
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| 32 | !! * Substitutions |
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| 33 | # include "domzgr_substitute.h90" |
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| 34 | # include "vectopt_loop_substitute.h90" |
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| 35 | !!---------------------------------------------------------------------- |
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[1566] | 36 | !! NEMO/OPA 3.2 , LODYC-IPSL (2009) |
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[1152] | 37 | !! $Id$ |
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[643] | 38 | !! Software governed by the CeCILL licence (modipsl/doc/NEMO_CeCILL.txt) |
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| 39 | !!---------------------------------------------------------------------- |
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| 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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| 57 | !! = 1/8 4th order finite differencing |
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| 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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| 64 | !! gamma1=1/4 and gamma2=1/8. |
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| 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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[1566] | 70 | USE oce, ONLY: zfu => ta ! use ta as 3D workspace |
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| 71 | USE oce, ONLY: zfv => sa ! use sa as 3D workspace |
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| 72 | !! |
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[643] | 73 | INTEGER, INTENT(in) :: kt ! ocean time-step index |
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[1566] | 74 | !! |
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| 75 | INTEGER :: ji, jj, jk ! dummy loop indices |
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| 76 | REAL(wp) :: zbu, zbv ! temporary scalars |
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| 77 | REAL(wp) :: zui, zvj, zfuj, zfvi, zl_u, zl_v ! temporary scalars |
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[643] | 78 | REAL(wp), DIMENSION(jpi,jpj,jpk) :: zfu_t, zfu_f ! temporary workspace |
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| 79 | REAL(wp), DIMENSION(jpi,jpj,jpk) :: zfv_t, zfv_f ! " " |
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| 80 | REAL(wp), DIMENSION(jpi,jpj,jpk) :: zfw, zfu_uw, zfv_vw |
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| 81 | REAL(wp), DIMENSION(jpi,jpj,jpk,2) :: zlu_uu, zlu_uv ! temporary workspace |
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| 82 | REAL(wp), DIMENSION(jpi,jpj,jpk,2) :: zlv_vv, zlv_vu ! temporary workspace |
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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_adv_ubs : UBS flux form momentum advection' |
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| 88 | IF(lwp) WRITE(numout,*) '~~~~~~~~~~~' |
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| 89 | ENDIF |
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| 90 | zfu_t(:,:,:) = 0.e0 |
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| 91 | zfv_t(:,:,:) = 0.e0 |
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| 92 | zfu_f(:,:,:) = 0.e0 |
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| 93 | zfv_f(:,:,:) = 0.e0 |
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[1566] | 94 | ! |
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[643] | 95 | zlu_uu(:,:,:,:) = 0.e0 |
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| 96 | zlv_vv(:,:,:,:) = 0.e0 |
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| 97 | zlu_uv(:,:,:,:) = 0.e0 |
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| 98 | zlv_vu(:,:,:,:) = 0.e0 |
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| 99 | |
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[1129] | 100 | IF( l_trddyn ) THEN ! Save ua and va trends |
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| 101 | zfu_uw(:,:,:) = ua(:,:,:) |
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| 102 | zfv_vw(:,:,:) = va(:,:,:) |
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| 103 | ENDIF |
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| 104 | |
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[1566] | 105 | ! ! =========================== ! |
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| 106 | DO jk = 1, jpkm1 ! Laplacian of the velocity ! |
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| 107 | ! ! =========================== ! |
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| 108 | ! ! horizontal volume fluxes |
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[643] | 109 | zfu(:,:,jk) = e2u(:,:) * fse3u(:,:,jk) * un(:,:,jk) |
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| 110 | zfv(:,:,jk) = e1v(:,:) * fse3v(:,:,jk) * vn(:,:,jk) |
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[1566] | 111 | ! |
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| 112 | DO jj = 2, jpjm1 ! laplacian |
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[643] | 113 | DO ji = fs_2, fs_jpim1 ! vector opt. |
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| 114 | 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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| 115 | 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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| 116 | zlu_uv(ji,jj,jk,1) = ( ub (ji,jj+1,jk)-2.*ub (ji,jj,jk)+ub (ji,jj-1,jk) ) * umask(ji,jj,jk) |
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| 117 | zlv_vu(ji,jj,jk,1) = ( vb (ji+1,jj,jk)-2.*vb (ji,jj,jk)+vb (ji-1,jj,jk) ) * vmask(ji,jj,jk) |
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| 118 | |
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| 119 | 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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| 120 | 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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| 121 | zlu_uv(ji,jj,jk,2) = ( zfu(ji,jj+1,jk)-2.*zfu(ji,jj,jk)+zfu(ji,jj-1,jk) ) * umask(ji,jj,jk) |
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| 122 | zlv_vu(ji,jj,jk,2) = ( zfv(ji+1,jj,jk)-2.*zfv(ji,jj,jk)+zfv(ji-1,jj,jk) ) * vmask(ji,jj,jk) |
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| 123 | END DO |
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| 124 | END DO |
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[1566] | 125 | END DO |
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| 126 | !!gm BUG !!! just below this should be +1 in all the communications |
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| 127 | CALL lbc_lnk( zlu_uu(:,:,:,1), 'U', -1.) ; CALL lbc_lnk( zlu_uv(:,:,:,1), 'U', -1.) |
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| 128 | CALL lbc_lnk( zlu_uu(:,:,:,2), 'U', -1.) ; CALL lbc_lnk( zlu_uv(:,:,:,2), 'U', -1.) |
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| 129 | CALL lbc_lnk( zlv_vv(:,:,:,1), 'V', -1.) ; CALL lbc_lnk( zlv_vu(:,:,:,1), 'V', -1.) |
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| 130 | CALL lbc_lnk( zlv_vv(:,:,:,2), 'V', -1.) ; CALL lbc_lnk( zlv_vu(:,:,:,2), 'V', -1.) |
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[643] | 131 | |
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[1566] | 132 | !!gm corrected: |
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| 133 | CALL lbc_lnk( zlu_uu(:,:,:,1), 'U', 1. ) ; CALL lbc_lnk( zlu_uv(:,:,:,1), 'U', 1. ) |
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| 134 | CALL lbc_lnk( zlu_uu(:,:,:,2), 'U', 1. ) ; CALL lbc_lnk( zlu_uv(:,:,:,2), 'U', 1. ) |
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| 135 | CALL lbc_lnk( zlv_vv(:,:,:,1), 'V', 1. ) ; CALL lbc_lnk( zlv_vu(:,:,:,1), 'V', 1. ) |
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| 136 | CALL lbc_lnk( zlv_vv(:,:,:,2), 'V', 1. ) ; CALL lbc_lnk( zlv_vu(:,:,:,2), 'V', 1. ) |
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| 137 | !!gm end |
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| 138 | |
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| 139 | ! ! ====================== ! |
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| 140 | ! ! Horizontal advection ! |
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| 141 | DO jk = 1, jpkm1 ! ====================== ! |
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| 142 | ! ! horizontal volume fluxes |
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[643] | 143 | zfu(:,:,jk) = 0.25 * e2u(:,:) * fse3u(:,:,jk) * un(:,:,jk) |
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| 144 | zfv(:,:,jk) = 0.25 * e1v(:,:) * fse3v(:,:,jk) * vn(:,:,jk) |
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[1566] | 145 | ! |
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| 146 | DO jj = 1, jpjm1 ! horizontal momentum fluxes at T- and F-point |
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[643] | 147 | DO ji = 1, fs_jpim1 ! vector opt. |
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| 148 | zui = ( un(ji,jj,jk) + un(ji+1,jj ,jk) ) |
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| 149 | zvj = ( vn(ji,jj,jk) + vn(ji ,jj+1,jk) ) |
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[1566] | 150 | ! |
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[643] | 151 | IF (zui > 0) THEN ; zl_u = zlu_uu(ji ,jj,jk,1) |
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| 152 | ELSE ; zl_u = zlu_uu(ji+1,jj,jk,1) |
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| 153 | ENDIF |
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| 154 | IF (zvj > 0) THEN ; zl_v = zlv_vv(ji,jj ,jk,1) |
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| 155 | ELSE ; zl_v = zlv_vv(ji,jj+1,jk,1) |
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| 156 | ENDIF |
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[1566] | 157 | ! |
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[643] | 158 | zfu_t(ji+1,jj ,jk) = ( zfu(ji,jj,jk) + zfu(ji+1,jj ,jk) & |
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| 159 | & - gamma2 * ( zlu_uu(ji,jj,jk,2) + zlu_uu(ji+1,jj ,jk,2) ) ) & |
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| 160 | & * ( zui - gamma1 * zl_u) |
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| 161 | zfv_t(ji ,jj+1,jk) = ( zfv(ji,jj,jk) + zfv(ji ,jj+1,jk) & |
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| 162 | & - gamma2 * ( zlv_vv(ji,jj,jk,2) + zlv_vv(ji ,jj+1,jk,2) ) ) & |
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| 163 | & * ( zvj - gamma1 * zl_v) |
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[1566] | 164 | ! |
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[643] | 165 | zfuj = ( zfu(ji,jj,jk) + zfu(ji ,jj+1,jk) ) |
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| 166 | zfvi = ( zfv(ji,jj,jk) + zfv(ji+1,jj ,jk) ) |
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| 167 | IF (zfuj > 0) THEN ; zl_v = zlv_vu( ji ,jj ,jk,1) |
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| 168 | ELSE ; zl_v = zlv_vu( ji+1,jj,jk,1) |
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| 169 | ENDIF |
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| 170 | IF (zfvi > 0) THEN ; zl_u = zlu_uv( ji,jj ,jk,1) |
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| 171 | ELSE ; zl_u = zlu_uv( ji,jj+1,jk,1) |
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| 172 | ENDIF |
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[1566] | 173 | ! |
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[643] | 174 | zfv_f(ji ,jj ,jk) = ( zfvi - gamma2 * ( zlv_vu(ji,jj,jk,2) + zlv_vu(ji+1,jj ,jk,2) ) ) & |
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| 175 | & * ( un(ji,jj,jk) + un(ji ,jj+1,jk) - gamma1 * zl_u ) |
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| 176 | zfu_f(ji ,jj ,jk) = ( zfuj - gamma2 * ( zlu_uv(ji,jj,jk,2) + zlu_uv(ji ,jj+1,jk,2) ) ) & |
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| 177 | & * ( vn(ji,jj,jk) + vn(ji+1,jj ,jk) - gamma1 * zl_v ) |
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| 178 | END DO |
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| 179 | END DO |
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[1566] | 180 | DO jj = 2, jpjm1 ! divergence of horizontal momentum fluxes |
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[643] | 181 | DO ji = fs_2, fs_jpim1 ! vector opt. |
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| 182 | zbu = e1u(ji,jj) * e2u(ji,jj) * fse3u(ji,jj,jk) |
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| 183 | zbv = e1v(ji,jj) * e2v(ji,jj) * fse3v(ji,jj,jk) |
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[1566] | 184 | ! |
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| 185 | ua(ji,jj,jk) = ua(ji,jj,jk) - ( zfu_t(ji+1,jj ,jk) - zfu_t(ji ,jj ,jk) & |
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| 186 | & + zfv_f(ji ,jj ,jk) - zfv_f(ji ,jj-1,jk) ) / zbu |
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| 187 | va(ji,jj,jk) = va(ji,jj,jk) - ( zfu_f(ji ,jj ,jk) - zfu_f(ji-1,jj ,jk) & |
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| 188 | & + zfv_t(ji ,jj+1,jk) - zfv_t(ji ,jj ,jk) ) / zbv |
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[643] | 189 | END DO |
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| 190 | END DO |
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[1566] | 191 | END DO |
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| 192 | IF( l_trddyn ) THEN ! save the horizontal advection trend for diagnostic |
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[1129] | 193 | zfu_uw(:,:,:) = ua(:,:,:) - zfu_uw(:,:,:) |
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| 194 | zfv_vw(:,:,:) = va(:,:,:) - zfv_vw(:,:,:) |
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| 195 | CALL trd_mod( zfu_uw, zfv_vw, jpdyn_trd_had, 'DYN', kt ) |
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| 196 | zfu_t(:,:,:) = ua(:,:,:) |
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| 197 | zfv_t(:,:,:) = va(:,:,:) |
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| 198 | ENDIF |
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| 199 | |
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[1566] | 200 | ! ! ==================== ! |
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| 201 | ! ! Vertical advection ! |
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| 202 | DO jk = 1, jpkm1 ! ==================== ! |
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| 203 | ! ! Vertical volume fluxesÊ |
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[643] | 204 | zfw(:,:,jk) = 0.25 * e1t(:,:) * e2t(:,:) * wn(:,:,jk) |
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[1566] | 205 | ! |
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| 206 | IF( jk == 1 ) THEN ! surface/bottom advective fluxes |
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| 207 | zfu_uw(:,:,jpk) = 0.e0 ! Bottom value : flux set to zero |
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[643] | 208 | zfv_vw(:,:,jpk) = 0.e0 |
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[1566] | 209 | ! ! Surface value : |
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| 210 | IF( lk_vvl ) THEN ! variable volume : flux set to zero |
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[643] | 211 | zfu_uw(:,:, 1 ) = 0.e0 |
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| 212 | zfv_vw(:,:, 1 ) = 0.e0 |
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[1566] | 213 | ELSE ! constant volume : advection through the surface |
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[643] | 214 | DO jj = 2, jpjm1 |
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| 215 | DO ji = fs_2, fs_jpim1 |
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| 216 | zfu_uw(ji,jj, 1 ) = 2.e0 * ( zfw(ji,jj,1) + zfw(ji+1,jj ,1) ) * un(ji,jj,1) |
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| 217 | zfv_vw(ji,jj, 1 ) = 2.e0 * ( zfw(ji,jj,1) + zfw(ji ,jj+1,1) ) * vn(ji,jj,1) |
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| 218 | END DO |
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| 219 | END DO |
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| 220 | ENDIF |
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[1566] | 221 | ELSE ! interior fluxes |
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[643] | 222 | DO jj = 2, jpjm1 |
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| 223 | DO ji = fs_2, fs_jpim1 ! vector opt. |
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| 224 | 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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| 225 | 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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| 226 | END DO |
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| 227 | END DO |
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| 228 | ENDIF |
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| 229 | END DO |
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[1566] | 230 | DO jk = 1, jpkm1 ! divergence of vertical momentum flux divergence |
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[643] | 231 | DO jj = 2, jpjm1 |
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| 232 | DO ji = fs_2, fs_jpim1 ! vector opt. |
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[1566] | 233 | ua(ji,jj,jk) = ua(ji,jj,jk) - ( zfu_uw(ji,jj,jk) - zfu_uw(ji,jj,jk+1) ) & |
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[643] | 234 | & / ( e1u(ji,jj) * e2u(ji,jj) * fse3u(ji,jj,jk) ) |
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[1566] | 235 | va(ji,jj,jk) = va(ji,jj,jk) - ( zfv_vw(ji,jj,jk) - zfv_vw(ji,jj,jk+1) ) & |
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[643] | 236 | & / ( e1v(ji,jj) * e2v(ji,jj) * fse3v(ji,jj,jk) ) |
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| 237 | END DO |
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| 238 | END DO |
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| 239 | END DO |
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[1566] | 240 | ! |
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| 241 | IF( l_trddyn ) THEN ! save the vertical advection trend for diagnostic |
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[1129] | 242 | zfu_t(:,:,:) = ua(:,:,:) - zfu_t(:,:,:) |
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| 243 | zfv_t(:,:,:) = va(:,:,:) - zfv_t(:,:,:) |
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| 244 | CALL trd_mod( zfu_t, zfv_t, jpdyn_trd_zad, 'DYN', kt ) |
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| 245 | ENDIF |
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[1566] | 246 | ! ! Control print |
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[1129] | 247 | IF(ln_ctl) CALL prt_ctl( tab3d_1=ua, clinfo1=' ubs2 adv - Ua: ', mask1=umask, & |
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| 248 | & tab3d_2=va, clinfo2= ' Va: ', mask2=vmask, clinfo3='dyn' ) |
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[1566] | 249 | ! |
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[643] | 250 | END SUBROUTINE dyn_adv_ubs |
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| 251 | |
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| 252 | !!============================================================================== |
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| 253 | END MODULE dynadv_ubs |
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